text:
Products for USB Sensing and Control
Products for USB Sensing and Control

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#### PHIDGETS Inc.

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## (±1V) Voltage Input Phidget

ID: VCP1002_0
Recommended for new designs: This product (or a similar replacement with a compatible form, fit and function) is estimated to be available for ten years or more.

Measure tiny voltage differences of up to ±1V with precision. This Phidget is isolated and plugs into a VINT port.

## $25.00 Quantity Available: 865 Qty Price 5$23.75
10 $22.50 25$20.00
50 $17.50 100$16.25
250 $15.00 500$13.75
1000 $12.50 The VCP1002 can be used to measure small voltage values up to ±1V. This Phidget connects to your computer through a VINT Hub. #### Features: • Select voltage range (±1V down to ±10mV) in software - Smaller range results in higher precision • Automatic mode - Continuously adjust the voltage range to improve measurement accuracy • Use with Current Sense Resistors to measure current in a circuit #### Technical Details: • Isolation - Protect your VINT Hub or computer from power surges and improve system stability by eliminating potential ground loops #### VINT Hubs This Phidget is a smart device that must be controlled by a VINT Hub. For more information about VINT, have a look at the VINT Primer. You can use a Phidget Cable to simply and easily connect the two devices. Here's a list of all of the different VINT Hubs currently available: Product Board Image Part Number Price Number of VINT Ports Controlled By HUB0000_0$30.00 6 USB (Mini-USB)
HUB5000_0 $60.00 6 Local Network (Ethernet or Wi-Fi) SBC3003_0$120.00 6

#### Phidget Cables

Use a Phidget cable to connect this device to the hub. You can solder multiple cables together in order to make even longer Phidget cables, but you should be aware of the effects of having long wires in your system.

Product Physical Properties
Image Part Number Price Cable Length
3002_0 $2.00 600 mm 3003_0$1.50 100 mm
3004_0 $3.00 3.5 m 3038_0$2.25 1.2 m
3039_0 $2.75 1.8 m CBL4104_0$1.75 300 mm
CBL4105_0 $2.00 900 mm CBL4106_0$2.50 1.5 m

## Step 1: Setup

### Select Device

Your Phidget must be connected to a device with a VINT port using a 3-wire Phidget cable.

## Step 1: Install Phidgets Library

Before you begin using your Phidgets, you will need to install the Phidget Library.

If you're unsure which one you should get, press ⊞ WIN + Pause/Break:

3a. Select Next

## Step 1: Install Phidgets Library

3b. Read the Licence Agreement. Select Next.

## Step 1: Install Phidgets Library

3c. Choose Installation Location. Select Next.

## Step 1: Install Phidgets Library

3d. Confirm Install

## Step 1: Install Phidgets Library

3e. Wait for Installation to complete. This should only take a few moments.

## Step 1: Install Phidgets Library

3f. Installation Complete. Close installation Window.

## Step 2: Connect Devices

● Connect USB Cable to your Windows Computer

● Connect VINT Device(s)

## Step 3: Verify Connection

1. Open the Phidgets Control Panel:

## Step 3: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

For more help installing in Windows (e.g. manual install, using a VM, etc.), visit this page:

## Step 1: Install Phidgets Library

Before you begin using your Phidgets, you will need to install the Phidget Library.

## Step 1: Install Phidgets Library

3a. Select Continue

## Step 1: Install Phidgets Library

3c. Here, you have the option to select the installation location. Select Install to continue.

## Step 1: Install Phidgets Library

3e. Wait for Installation to complete. This should only take a few moments.

## Step 1: Install Phidgets Library

3f. You may see a message that the extension has been blocked. Select Open Security Preferences.

## Step 1: Install Phidgets Library

3g. Beside the message for Phidgets Inc, Click Allow.

## Step 1: Install Phidgets Library

3h. Installation Complete, Click Close.

## Step 1: Install Phidgets Library

3i. To delete the installer, click Move to Trash.

## Step 2: Connect Devices

● Connect USB Cable to your Mac

● Connect VINT Device(s)

## Step 3: Verify Connection

1. Open the Phidgets Control Panel:

## Step 3: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Step 1: Install Phidgets Library

1. First, you need to install the libusb-1.0 development libraries. For example, in Debian based distributions:

apt-get install libusb-1.0-0-dev

You’ll also need a C compiler and builder, if you don’t already have one installed.

apt-get install gcc
apt-get install make

## Step 1: Install Phidgets Library

3. Use the following commands in the location you unpacked to install the library:

./configure
make
sudo make install

## Step 1: Install Phidgets Library

4. (Optional) You can also download and unpack the following optional packages:

phidget22networkserver - Phidget Network Server, which enables the use of Phidgets over your network

phidget22admin - Admin tool to track who is connected to your Phidgets when using the network server

libphidget22extra - Required for phidget22networkserver and phidget22admin

libphidget22java - The Java libraries for Phidget22

For installation instructions for these packages, see the README file included with each one.

## Step 2: Connect Devices

● Connect USB Cable to your Linux Computer

● Connect VINT Device(s)

## Step 3: Verify Connection

1. The easiest way to verify that your libraries are working properly is to compile and run an example program. Download and unpack this C example that will detect any Phidget:

## Step 3: Verify Connection

2. Next, open the terminal in the location where you unpacked the example. Compile and run using:

gcc HelloWorld.c -o HelloWorld -lphidget22
sudo ./HelloWorld

ou should receive a “Hello” line for each Phidget channel that is discovered:

I don’t see any Phidgets show up in the HelloWorld example

You need to run it with sudo in order to be able to access USB devices. In order to use Phidgets without sudo, you need to set your udev rules. See the Advanced Information page on the final slide of this guide for details.

## Done!

If you're able to see your devices in the Hello World example, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Step 1: Install Phidgets Library

Before you begin using your Phidgets, you will need to install the Phidget Library.

If you're unsure which one you should get, press ⊞ WIN + Pause/Break:

3a. Select Next

## Step 1: Install Phidgets Library

3b. Read the Licence Agreement. Select Next.

## Step 1: Install Phidgets Library

3c. Choose Installation Location. Select Next.

## Step 1: Install Phidgets Library

3d. Select Next to confirm install.

## Step 1: Install Phidgets Library

3e. Wait for Installation to complete. This should only take a few moments.

## Step 1: Install Phidgets Library

3f. Installation Complete. Close installation Window.

## Step 2: Connect Devices

● Connect Power Jack

● Connect VINT Device(s)

● Connect Ethernet to a Router or Switch (optional)

## Step 3: Verify Connection

Choose a setup method:

## Step 3: Connect Wireless

1. When you connect the power supply to the HUB5000, the red LED should turn on.

## Step 3: Connect Wireless

2. On your mobile device, go to the Wi-Fi settings and connect to the HUB5000:

## Step 3: Connect Wireless

4. Once your device is connected to the HUB5000’s WiFi signal:

Click on the WiFi network and find an option that says “Manage router” or “Visit homepage”.

Go to your internet browser and type 192.168.100.1 in the address bar.

## Step 3: Connect Wireless

5. Create a password for your HUB5000. You'll use it to access the Configure Page from now on.

## Step 3: Connect Wireless

6. Navigate to the network page. Change the Mode to Client.

## Step 3: Connect Wireless

7. Enter your Wifi Network details and click Save & Apply. It may take a few minutes for your Phidgets to appear in the Phidget Control Panel, which we’ll check in the next step.

## Step 4: Verify Connection

1. Open the Phidgets Control Panel:

## Step 4: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

For more help installing in Windows (e.g. manual install, using a VM, etc.), visit this page:

## Step 3: Connect Wireless

1. When you connect the power supply to the HUB5000, the red LED should turn on.

## Step 3: Connect Wireless

3. Create a password for your HUB5000. You'll use this password to access the Configure Page from now on.

## Step 3: Connect Wireless

4. Navigate to the network page. Change the Mode to Client.

## Step 3: Connect Wireless

5. Enter your Wifi Network details to use your Hub wirelessly and click Save & Apply. You can then disconnect the ethernet cable.

It may take a few minutes for your Phidgets to appear in the Phidget Control Panel, which we’ll check in the next step.

## Step 4: Verify Connection

1. Open the Phidgets Control Panel:

## Step 4: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

For more help installing in Windows (e.g. manual install, using a VM, etc.), visit this page:

## Step 1: Install Phidgets Library

Before you begin using your Phidgets, you will need to install the Phidget Library.

## Step 1: Install Phidgets Library

3a. Select Continue

## Step 1: Install Phidgets Library

3c. Here, you have the option to select the installation location. Select Install.

## Step 1: Install Phidgets Library

3e. Wait for Installation to complete. This should only take a few moments.

## Step 1: Install Phidgets Library

3f. You may see a message that the extension has been blocked. Select Open Security Preferences.

## Step 1: Install Phidgets Library

3g. Beside the message for Phidgets Inc, Click Allow.

## Step 1: Install Phidgets Library

3h. Installation Complete, Click Close.

## Step 1: Install Phidgets Library

3i. To delete the installer, click Move to Trash.

## Step 2: Connect Devices

● Connect Power Jack

● Connect VINT Device(s)

● Connect Ethernet to a Router or Switch (optional)

## Step 3: Verify Connection

Choose a setup method:

## Step 3: Connect Wireless

1. When you connect the power supply to the HUB5000, the red LED should turn on.

## Step 3: Connect Wireless

2. On your mobile device, go to the Wi-Fi settings and connect to the HUB5000:

## Step 3: Connect Wireless

4. Once your device is connected to the HUB5000’s WiFi signal:

Click on the WiFi network and find an option that says “Manage router” or “Visit homepage”.

Go to your internet browser and type 192.168.100.1 in the address bar.

## Step 3: Connect Wireless

5. Create a password for your HUB5000. You'll use this password to access the Configure Page from now on.

## Step 3: Connect Wireless

6. Navigate to the network page. Change the Mode to Client.

## Step 3: Connect Wireless

7. Enter your Wifi Network details and click Save & Apply. It may take a few minutes for your Phidgets to appear in the Phidget Control Panel, which we’ll check in the next step.

## Step 4: Verify Connection

1. Open the Phidget Control Panel:

## Step 4: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Step 3: Connect Wireless

1. When you connect the power supply to the HUB5000, the red LED should turn on.

## Step 3: Connect Wireless

3. Create a password for your HUB5000. You'll use this password to access the Configure Page from now on.

## Step 3: Connect Wireless

4. Navigate to the network page. Change the Mode to Client.

## Step 3: Connect Wireless

5. Enter your Wifi Network details to use your Hub wirelessly and click Save & Apply. You can then disconnect the ethernet cable.

It may take a few minutes for your Phidgets to appear in the Phidget Control Panel, which we’ll check in the next step.

## Step 4: Verify Connection

1. Open the Phidget Control Panel:

## Step 4: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Step 1: Install Phidgets Library

1. First, you need to install the libusb-1.0 development libraries. For example, in Debian based distributions:

apt-get install libusb-1.0-0-dev

You’ll also need a C compiler and builder, if you don’t already have one installed.

apt-get install gcc
apt-get install make

## Step 1: Install Phidgets Library

3. Use the following commands in the location you unpacked to install the library:

./configure
make
sudo make install

## Step 1: Install Phidgets Library

4. (Optional) You can also download and unpack the following optional packages:

phidget22networkserver - Phidget Network Server, which enables the use of Phidgets over your network

phidget22admin - Admin tool to track who is connected to your Phidgets when using the network server

libphidget22extra - Required for phidget22networkserver and phidget22admin

libphidget22java - The Java libraries for Phidget22

For installation instructions for these packages, see the README file included with each one.

## Step 2: Connect Devices

● Connect Power Jack

● Connect VINT Device(s)

● Connect Ethernet to a Router or Switch (optional)

## Step 3: Verify Connection

Choose a setup method:

## Step 3: Connect Wireless

1. When you connect the power supply to the HUB5000, the red LED should turn on.

## Step 3: Connect Wireless

2. On your mobile device, go to the Wi-Fi settings and connect to the HUB5000:

## Step 3: Connect Wireless

4. Once your device is connected to the HUB5000’s WiFi signal:

Click on the WiFi network and find an option that says “Manage router” or “Visit homepage”.

Go to your internet browser and type 192.168.100.1 in the address bar.

## Step 3: Connect Wireless

5. Create a password for your HUB5000. You'll use this password to access the Configure Page from now on.

## Step 3: Connect Wireless

6. Navigate to the network page. Change the Mode to Client.

## Step 3: Connect Wireless

7. Enter your Wifi Network details and click Save & Apply. It may take a few minutes for your Phidgets to appear in the Phidget Control Panel, which we’ll check in the next step.

## Step 4: Verify Connection

1. The easiest way to verify that your libraries are working properly is to compile and run an example program. Download and unpack this C example that will detect any Phidget:

## Step 3: Verify Connection

2. Next, open the terminal in the location where you unpacked the example. Compile and run using:

gcc HelloWorld.c -o HelloWorld -lphidget22
sudo ./HelloWorld

ou should receive a “Hello” line for each Phidget channel that is discovered:

I don’t see any Phidgets show up in the HelloWorld example

You need to run it with sudo in order to be able to access USB devices. In order to use Phidgets without sudo, you need to set your udev rules. See the Advanced Information page on the final slide of this guide for details.

## Done!

If you're able to see your devices in the Hello World example, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Step 3: Connect Wireless

1. When you connect the power supply to the HUB5000, the red LED should turn on.

## Step 3: Connect Wireless

3. Create a password for your HUB5000. You'll use this password to access the Configure Page from now on.

## Step 3: Connect Wireless

4. Navigate to the network page. Change the Mode to Client.

## Step 3: Connect Wireless

5. Enter your Wifi Network details to use your Hub wirelessly and click Save & Apply. You can then disconnect the ethernet cable.

It may take a few minutes for your Phidgets to appear in the Phidget Control Panel, which we’ll check in the next step.

## Step 4: Verify Connection

1. The easiest way to verify that your libraries are working properly is to compile and run an example program. Download and unpack this C example that will detect any Phidget:

## Step 3: Verify Connection

2. Next, open the terminal in the location where you unpacked the example. Compile and run using:

gcc HelloWorld.c -o HelloWorld -lphidget22
sudo ./HelloWorld

ou should receive a “Hello” line for each Phidget channel that is discovered:

I don’t see any Phidgets show up in the HelloWorld example

You need to run it with sudo in order to be able to access USB devices. In order to use Phidgets without sudo, you need to set your udev rules. See the Advanced Information page on the final slide of this guide for details.

## Done!

If you're able to see your devices in the Hello World example, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Step 1: Install Phidgets Library

Before you begin using your Phidgets, you will need to install the Phidget Library.

If you're unsure which one you should get, press ⊞ WIN + Pause/Break:

3a. Select Next.

## Step 1: Install Phidgets Library

3b. Read the Licence Agreement. Select Next.

## Step 1: Install Phidgets Library

3c. Choose Installation Location. Select Next.

3d. Select Next.

## Step 1: Install Phidgets Library

3e. Wait for Installation to complete. This should only take a few moments.

## Step 1: Install Phidgets Library

3f. Installation Complete. Close installation Window.

## Step 2: Connect Devices

● Connect Power Jack

● Connect VINT Device(s)

● Connect Ethernet to a Router or Switch in the same network as your Windows PC

## Step 3: Verify Connection

1. Open the Phidgets Control Panel:

## Step 3: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

Now that the SBC's ethernet connection is verified, it can be connected to wifi.

If you don't have a USB wifi adapter or you're planning to stay on ethernet, you can scroll down to

## Step 4: Connect Wireless

2. Create a password for your SBC. You'll use this to access the configuration page from now on.

## Step 4: Connect Wireless

3. Navigate to Network -> Wireless. Select your Network, enter the wifi password and select Add This Network.

## Step 4: Connect Wireless

4. Scroll down to your saved networks, click on your network and select Join This Network.

## Step 4: Connect Wireless

5. It should now say connected in the status column.

You can now unplug the ethernet cable.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

For more help installing in Windows (e.g. manual install, using a VM, etc.), visit this page:

## Step 1: Install Phidgets Library

Before you begin using your Phidgets, you will need to install the Phidget Library.

## Step 1: Install Phidgets Library

3a. Select Continue

## Step 1: Install Phidgets Library

3c. Here, you have the option to select the installation location. Select Install.

## Step 1: Install Phidgets Library

3e. Wait for Installation to complete. This should only take a few moments.

## Step 1: Install Phidgets Library

3f. You may see a message that the extension has been blocked. Select Open Security Preferences.

3g. Click Allow.

## Step 1: Install Phidgets Library

3h. Installation Complete, Click Close.

## Step 1: Install Phidgets Library

3i. To delete the installer, click Move to Trash.

## Step 2: Connect Devices

● Connect Power Jack

● Connect VINT Device(s)

● Connect Ethernet to a Router or Switch in the same network as your Mac

## Step 3: Verify Connection

1. Open the Phidget Control Panel:

## Step 3: Verify Connection

2. If connected, your Phidgets will appear in the Phidget Control Panel.

Now that the SBC's ethernet connection is verified, it can be connected to wifi.

If you don't have a USB wifi adapter or you're planning to stay on ethernet, you can scroll down to

## Step 4: Connect Wireless

2. Create a password for your SBC. You will use this to access the configuration page from now on.

## Step 4: Connect Wireless

3. Navigate to Network -> Wireless. Select your Network, enter the wifi password and select Add This Network.

## Step 4: Connect Wireless

4. Scroll down to your saved networks, click on your network and select Join This Network.

## Step 4: Connect Wireless

5. It should now say connected in the status column.

You can now unplug the ethernet cable.

## Done!

If you're able to see and interact with your devices in the Phidget Control Panel, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Step 1: Install Phidgets Library

1. First, you need to install the libusb-1.0 development libraries. For example, in Debian based distributions:

apt-get install libusb-1.0-0-dev

You’ll also need a C compiler and builder, if you don’t already have one installed.

apt-get install gcc
apt-get install make

## Step 1: Install Phidgets Library

3. Use the following commands in the location you unpacked to install the library:

./configure
make
sudo make install

## Step 1: Install Phidgets Library

4. (Optional) You can also download and unpack the following optional packages:

phidget22networkserver - Phidget Network Server, which enables the use of Phidgets over your network

phidget22admin - Admin tool to track who is connected to your Phidgets when using the network server

libphidget22extra - Required for phidget22networkserver and phidget22admin

libphidget22java - The Java libraries for Phidget22

For installation instructions for these packages, see the README file included with each one.

## Step 2: Connect Devices

● Connect Power Jack

● Connect VINT Device(s)

● Connect Ethernet to a Router or Switch in the same network as your Linux machine

## Step 3: Verify Connection

1. The easiest way to verify that your libraries are working properly is to compile and run an example program. Download and unpack this C example that will detect any Phidget:

## Step 3: Verify Connection

2. Next, open the terminal in the location where you unpacked the example. Compile and run using:

gcc HelloWorld.c -o HelloWorld -lphidget22
sudo ./HelloWorld

If everything is working, you should receive a “Hello” line for each Phidget channel that is discovered:

I don’t see any Phidgets show up in the HelloWorld example

You need to run it with sudo in order to be able to access USB devices. In order to use Phidgets without sudo, you need to set your udev rules. See the Advanced Information page on the final slide of this guide for details.

Now that the SBC's ethernet connection is verified, it can be connected to wifi.

If you don't have a USB wifi adapter or you're planning to stay on ethernet, you can scroll down to

## Step 4: Connect Wireless

If you're using a terminal-only Linux machine, use the browser on your phone instead.

(If you use a phone, you need to enter the IP address your router assigned to the SBC instead of phidgetsbc.local)

## Step 4: Connect Wireless

2. Create a password for your SBC. You will use this to access the configuration page from now on.

## Step 4: Connect Wireless

3. Navigate to Network -> Wireless. Select your Network, enter the wifi password and select Add This Network.

## Step 4: Connect Wireless

4. Scroll down to your saved networks, click on your network and select Join This Network.

## Step 4: Connect Wireless

5. It should now say connected in the status column.

You can now unplug the ethernet cable.

## Step 4: Connect Wireless

6. Run the HelloWorld example again to confirm that your Phidgets are accessible over wifi.

## Done!

If you're able to see your devices in the Hello World example, you're done with the Setup part of this guide.

Scroll down to Part 2: Using Your Phidget for the next step.

## Part 2: Using Your Phidget

The VCP1002 allows you to measure voltages up to ±1V. This Phidget is ideal for small voltage monitoring applications. You can manually select the voltage range (±1V down to ±10mV) in your program to maximize resolution, or use Automatic mode which constantly adjusts the range based on the last voltage measurement.

### Explore Your Phidget Channels Using The Control Panel

1. Open your Control Panel, and you will find the 10-bit (±1V) Voltage Input Phidget channel:

2. Double click on the channel to open an example program. This channel belongs to the Voltage Input channel class:

10-bit (±1V) Voltage Input Phidget : Measures the voltage across the VCP1002’s terminals

In your Control Panel, double click on "10-bit (±1V) Voltage Input Phidget":

## Part 4: Advanced Topics and Troubleshooting

How do I know what channel, serial number, or hub port to use in my program?

Before you open a Phidget channel in your program, you can set these properties to specify which channel to open. You can find this information through the Control Panel.

1. Open the Control Panel and double-click on the red map pin icon:

2. The Addressing Information window will open. Here you will find all the information you need to address your Phidget in your program.

See the Phidget22 API for your language to determine exact syntax for each property.

Setting the Change Trigger and Data Interval

The Change Trigger is the minimum change in the sensor data needed to trigger a new data event. The Data Interval is the time (in ms) between data events sent out from your Phidget. You can modify one or both of these values to achieve different data outputs. You can learn more about these two properties here.

How can I plot or record sensor data?

In the Phidget Control Panel, open the channel for your device and click on the icon next to the data type that you want to plot. This will open up a new window:

If you need more complex functionality such as logging multiple sensors to the same sheet or performing calculations on the data, you'll need to write your own program. Generally this will involve addressing the correct channel, opening it, and then creating an Event Handler and adding graphing/logging code to it.

The quickest way to get started is to download some sample code for your desired programming language and then search google for logging or plotting in that language (e.g. "how to log to csv in python") and add the code to the existing change handler.

Isolation

The VCP1002 is electrically isolated. A power surge in the circuit being measured would only affect the VCP1002, so your VINT Hub or computer will remain unharmed. Having isolation also helps prevent the formation of ground loops in your system.

With isolation on the VCP1002, you can measure the voltage differential between two points of a circuit regardless of their relation to ground. The voltage differential between those points must be within the specification of the sensor.

For example, in the pictured battery charging circuit, there is sufficient complexity between the current sense resistor (Rsense) and VINT Hub that directly measuring the voltage with a non-isolated sensor could be a risky proposition. However, with VCP1002, the voltage across the resistor may be measured directly, ignoring the circuits in between.

Measuring the voltage across "Rsense" in this circuit is made easy through isolation!
Current Sense Resistors

The VCP1002 is made to measure small voltages anywhere in a circuit. As a result, the VCP1002 is ideal for use with current sense resistors to measure current. For an in-depth look at how to use current sense resistors with the VCP1002, see our article about Current Sense Resistors.

#### Product Specifications

Sensor Properties
Sensor Type Voltage (DC)
Board Properties
Controlled By VINT
Voltage Sensor
Voltage Difference Max ± 1 V DC
Withstand Voltage Max ± 50 V DC
Sampling Interval Max 60 s/sample
Sampling Interval Min 40 ms/sample
Sensor Input Impedance 1 MΩ
Measurement Error Max 0.1 %
Number of Voltage Inputs 1
Voltage Resolution 1 mV DC
±10 mV Range
Voltage Resolution 300 nV DC
Voltage Offset Max 25 μV DC
Measurement Error Max 0.5 %
Voltage Noise 6 μV DC
±40 mV Range
Voltage Resolution 1.2 μV DC
Voltage Offset Max 40 μV DC
Measurement Error Max 0.25 %
Voltage Noise 25 μV DC
±200 mV Range
Voltage Resolution 6 μV DC
Voltage Offset Max 200 μV DC
Measurement Error Max 0.25 %
Voltage Noise 100 μV DC
±1 V Range
Voltage Resolution 28.8 μV DC
Voltage Offset Max 1 mV DC
Measurement Error Max 0.3 %
Voltage Noise 500 μV DC
Electrical Properties
Current Consumption Max 12 mA
Physical Properties
Recommended Wire Size 16 - 26 AWG
Operating Temperature Min -40 °C
Operating Temperature Max 85 °C
Customs Information
American HTS Import Code 9030.33.38.00
Country of Origin CN (China)

#### Product History

Date Board Revision Device Version Comment
June 20170106Product Release

#### Software Objects

Channel NameAPIChannel
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text:
# American Institute of Mathematical Sciences

2002, 1(4): 513-530. doi: 10.3934/cpaa.2002.1.513

## Existence result for a class of nonconservative and nonstrictly hyperbolic systems

 1 Centre de Mathematiques Appliquees, Ecole Polytechnique, and Dipartimento di Matematica Pura e Appl., Universita di Modena, Via Campi 213/B, 41100 Modena, Italy 2 Centre de Mathématiques Appliquées, and Centre National de la Recherche Scientifique, UMR. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France

Received  March 2002 Revised  July 2002 Published  September 2002

We consider the class of nonconservative hyperbolic systems

$\partial_t u+A(u) \partial_x u =0,\quad\partial_t v + A(u) \partial_x v =0,$

where $u=u(x,t),\quad v=v(x,t)\in\mathbb R^N$ are the unknowns and $A(u)$ is a strictly hyperbolic matrix. Relying on the notion of weak solution proposed by Dal Maso, LeFloch, and Murat ("Definition and weak stability of nonconservative products", J. Math. Pures Appl. 74 (1995), 483--548), we establish the existence of weak solutions for the corresponding Cauchy problem, in the class of bounded functions with bounded variation. The main steps in our proof are as follows:
(i) We solve the Riemann problem based on a prescribed family of paths.
(ii) We derive a uniform bound on the total variation of corresponding wave-front tracking approximations $u^h$, $v^h$.
(iii) We justify rigorously the passage to the limit in the nonconservative product $A(u^h) \partial_x v^h$, based on the local uniform convergence properties of $u^h$, by extending an argument due to LeFloch and Liu ("Existence theory for nonlinear hyperbolic systems in nonconservative form", Forum Math. 5 (1993), 261--280). Our results provide a generalization to the existence theorem established earlier in the scalar case ($N=1$) by the second author ("An existence and uniqueness result for two nonstrictly hyperbolic systems", IMA Volumes in Math. and its Appl. 27, "Nonlinear evolution equations that change type", ed. B.L. Keyfitz and M. Shearer, Springer Verlag, 1990, pp. 126--138.)

Citation: Graziano Crasta, Philippe G. LeFloch. Existence result for a class of nonconservative and nonstrictly hyperbolic systems. Communications on Pure & Applied Analysis, 2002, 1 (4) : 513-530. doi: 10.3934/cpaa.2002.1.513
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2017 Impact Factor: 0.884

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text:
Alternating magnetic field

1. Dec 11, 2008

FourierX

1. The problem statement, all variables and given/known data

A conducting disk (very thin) of thickness h, diameter D, and conductivity $$\sigma$$ is placed in a uniform alternating magnetic field B = Bosin$$\omega$$t parallel to the axis of the disk.
Determine the induced current density as a function of the distance from the axis of the disk. Also mention the direction of the current.

2. Relevant equations

$$\oint$$B.da = $$\mu_o$$ Ienc

3. The attempt at a solution

From ampere's law, i derirved $$\nabla$$xB = $$\mu_o$$J. Is my approach correct ? How do i make use of thickness, diameter and conductivity of the disk?

2. Dec 12, 2008

wdednam

Hi FourierX,

Your relevant equation, Ampere's law, might not be very helpful here. I suggest you use Faraday's law of induction instead. The relation between the electric field and current density, J = sigma*E might also come in handy.

Good luck,

Wynand.

3. Dec 12, 2008

FourierX

Thank for the reply. But i wonder how?

4. Dec 12, 2008

wdednam

Hi,

You've got to ask yourself the following questions: Which phenomenon am I dealing with here? What is the CHANGING (clue) magnetic field going to do to the conducting disk? In general, what do changing magnetic fields do?

Hope this helps,

Wynand.

5. Dec 13, 2008

FourierX

Thanks bud!

Ok, here is what i did.

-calculated the flux (area of the disk times the magnetic field)
- used Faraday's law (emf = negative time derivative of magnetic flux)
- I = emf/R = emf (conductivity)

does it seem correct? So far the, the current is expressed as a function of time. Any idea on how to express it as a function of distance from the axis of the disk?

6. Dec 13, 2008

wdednam

No problem!

Spot on with steps 1 and 2 of your calculations.

Okay, according to the problem statement we should calculate the current density J as a function of the distance from the disk's axis, so I don't think you need to worry about finding the current I.

So, from step 2 of your calculations we need to get to J as a function of the time derivative of the flux and the distance from the disk's axis.

Now, a changing magnetic field not only induces an emf, but also an Electric field, E. If you can find the relationship between those (hint: it involves a line integral around a closed path), and use the relationship between E and J, i.e. J = conductivity*E, then your problem is basically solved.

You'll notice that the thickness h of the disk won't appear in your answer for J. If you were required to calculate I, the current, instead, then it would appear in your answer for that.

Hope this helps,

Cheers,

Wynand.


text:
# Unique type ID, no RTTI

Following my answer to Unique type ID in C++, I have worked towards a "safer" version that I am posting here.

This is a lightweight type that can store a unique (also across compilation units) ID per type for use at runtime, without RTTI.

Instead of using a built-in type for ID representation that is also accessible to the end user, a specific class type_id_t provides the external representation of the ID and encapsulates the actual storage type (a function pointer) that is not accessible.

A helper function template call type_id<T>() returns a type_id_t containing the ID of type T.

Hence, the following operations are only provided:

• construction only by calling type_id function.
• copy/move construction, as implicitly defined
• copy/move assignment, as implicitly defined
• comparison operators == and != between two type_id_t's

There is no default constructor for type_id_t.

Here is the implementation:

class type_id_t
{
using sig = type_id_t();

sig* id;
type_id_t(sig* id) : id{id} {}

public:
template<typename T>
friend type_id_t type_id();

bool operator==(type_id_t o) const { return id == o.id; }
bool operator!=(type_id_t o) const { return id != o.id; }
};

template<typename T>
type_id_t type_id() { return &type_id<T>; }

It is interesting that function type_id returns a (function) pointer to itself, encapsulated into a type_id_t. No nasty type casting is necessary.

This is not a mechanism that provides runtime identification of a (polymorphic) object's type, but can be used as a low-level tool to build such functionality. I actually made this for the needs of my recent any, and then improved it.

Just for demonstration, we can store the ID of a number of types e.g. in a vector:

template<typename... T>
std::vector<type_id_t>
make_ids() { return {type_id<T>()...}; }

Later, we can compare the stored IDs to the ID of a given type:

template<typename T, typename A>
void comp_ids(const A& a)
{
for (auto i : a)
std::cout << (type_id<T>() == i) << " ";
std::cout << std::endl;
}

and get the following:

auto ids = make_ids<
int, bool, double const&, int&&, char(&)[8],
int, void(int), unsigned char**, std::vector<void(*)()>, double[4][8]
>();

comp_ids<int>(ids);  // output: 1 0 0 0 0 1 0 0 0 0

Here is a live example.

Any comments are welcome.

• the type id trick won't work across shared libraries. – user1095108 May 29 '14 at 8:46
• @user1095108 Are you sure? I have posted a specific question on this. There has been some discussion and it appears that it will work. Bottomline is that templates are defined as weak symbols and are merged into one definition at link time according to iso 3.2/5. – iavr May 29 '14 at 9:00
• Hi, is there any way, how to access type of type_id<T> later in the class? For debug purposes, would be great to be able to access some stringable object id (not pointer address). In VisualStudio, I see that sig has type t1 = {id=0x01bfdc52 {type_id<struct ....stTest>(void)} }. But I'm not able to get this value through typeid() in any way. Thanks. – Ludek Vodicka Mar 28 '19 at 8:33

## 2 Answers

The first thing I notice when looking at this code is the lack of documentation.

I would provide some more operators. Specifically I would go for operator< so type_id_t is usable as key for std::map and you should think about specializing std::hash so the class can be used with hash maps.

As the code is pretty short I don't find any more to say about it.

Btw.: Well done. I like this solution very much.

• Thanks, very good point about operator< and std::hash! I thought == and != should be enough for identification, but being able to use ID as key in an associative container sounds very essential. As for documentation, this is my weakest point--I only hope this page could be seen as some form of documentation :-) – iavr Apr 30 '14 at 18:07

This is very nice, however, I usually just use:

using typeid_t = void const*;

template <typename T>
typeid_t type_id() noexcept
{
static char const type_id;

return &type_id;
}

The void const* pointers can be compared and hashed and cannot be dereferenced without casting. Good enough for me. The solution also avoids casts, just like your question.

Alternatively:

using typeid_t = void(*)();

template <typename T>
typeid_t type_id() noexcept
{
return typeid_t(type_id<T>);
}

• Doesn't work across the shared libraries. The one with the function template instantiation address does work however. – Velkan Jan 18 '17 at 9:04
• could be you did not export the function. Anyway, I've provided an alternative now. – user1095108 Jan 18 '17 at 9:28
• Doesn't work with VS :( it always return same address. – Dawid Drozd Jan 20 '19 at 19:25
• @DawidDrozd if you instantiate it with the same T, this is what it should do. – user1095108 Jan 20 '19 at 20:48
• @DawidDrozd put static` in front of the function definition, there's always a way around vc++ strangeness. I always use this function as a class member not as a free function. – user1095108 Jan 21 '19 at 15:50


text:
Question
When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of the bolt. (a) How much torque are you exerting in newton × meters (relative to the center of the bolt)? (b) Convert this torque to footpounds.
1. $23.1 \textrm{ N}\cdot\textrm{m}$
2. $17.0 \textrm{ ft}\cdot\textrm{lbs}$

Note: The video incorrectly shows the conversion to $\textrm{ft}\cdot\textrm{lbs}$ by dividing instead of multiplying by 0.7356. The calculator screenshot has been corrected, and the final answer above is correct.

Solution Video

# OpenStax College Physics Solution, Chapter 9, Problem 2 (Problems & Exercises) (0:34)

Rating

1 vote with a rating of 5

## Calculator Screenshots

Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to calculate the torque applied about the bolt when applying a force of 165 newtons on the wrench at a distance that's perpendicular to the pivot, 0.140 meters away. So we multiply these two together and get 23.1 newton meters and converting that into foot pounds by multiplying by 1 ft lbs for every 0.73756 newton meters, this is 31.3 ft lbs.


text:
# Numerical computation stability issue

We have a problem to find $x$ such that $$\sum_{i}\left(\frac{a_i}{x}\right)^\lambda= \sum_{j}\left(\frac{b_j}{x}\right)^{-\lambda}$$

$a_i < x < b_j$

$a_i \approx x \approx b_j$

We get analytic solution: $$x = \left[\frac{\sum_{i}a_i^\lambda}{\sum_{j}b_j^{-\lambda}}\right]^{\frac{1}{2\lambda}}$$

But since $a_i,b_j,x,\lambda \approx 10^3$ we cannot evaluate this formula because of numerical overflow ($a_i ^ \lambda \approx 1000^{1000}$)

-
There's also the Computation Science StackExchange (scicomp.stackexchange.com) in Beta that can help with this sort of question (and needs some more love to stay alive!). Just sayin' :) – Damien Aug 27 '12 at 11:04

The expression for $x$ is invariant under change of scale: $a'_i= s a_i$, $b'_j= s b_j$. So, use $s=10^{-3}$ and get those numbers close to 1. This probably helps.
This is similar to what lhf said, but it might help. Set $A=\max_i a_i$ and $B=\max_i b_i$, then $$x=\sqrt{\frac{A}{B}}\left[\frac{\sum_i\left(\frac{a_i}{A}\right)^\lambda}{\sum_i\left(\frac{b_i}{B}\right)^\lambda}\right]^\frac{1}{2\lambda}$$ I think that this should get you decent stability and keep the computation from overflowing.


text:
# Seminar: Goldie rank quasipolynomials via lattice point enumeration

Speaker: Joanna Meinel (Max Planck Institute for Mathematics, Bonn)

2012.09.20 | Christine Dilling

 Date Wed 15 Feb Time 14:15 — 15:15 Location Aud. D3 (1531-215)

Abstract

In 1998, Musson and Van den Bergh gave a classification of primitive ideals (the annihilators of simple modules) for a class of algebras related to the Weyl algebra $~k[x_1,...,x_n,\partial_1,...,\partial_n]$. Similar to the case of universal enveloping algebras of semisimple complex Lie algebras, it suffices to look only at some of the simple modules to get a description of all primitive ideals. For the Weyl algebra this description can be made explicit in terms of lattice points and polyhedrons, which we will illustrate by a small example.
Then we want to study the quotients of our algebra with respect to the primitive ideals: Using the geometrical picture and Ehrhart theory, we construct for each nice family of such quotients a quasipolynomial that gives the Goldie rank of each quotient.

Seminar, Staff, Public/media


text:
Chapter 14, Problem 72E

### Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

Chapter
Section

### Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

# A solution is made by adding 50.0 mL of 0.200 M acetic acid (K4 = 1.8 × 10–3) to 50.0 mL of 1.00 × 10–3 M HCl  a. Calculate the pH of the solution  b. Calculate the acetate ion concentration.

(b)

Interpretation Introduction

Interpretation:

A solution is made by adding 50.0 mL of 0.200M Acetic acid to 50mL of 1×10-3M HCl .

1. (a) pH of the solution is to be calculated.
2. (b) Acetate ion concentration to be calculated.

Concept introduction:

The pH of a solution is define as a figure that expresses the acidity of the alkalinity of a given solution.

The pH of a solution is calculated by the formula, pH=log[H+]

The number of moles of a solute is calculated by the formula,

Molesofsolute=Volume(L)×Molarity

Explanation

To determine: Equilibrium concentration of Acetate ion

The moles of CH3COOH are 0.01mol_ and that of HCl are 5.0×10-5mol_ .

Given data

Volume of CH3COOH is 50.0mL(0.050L) .

Concentration of CH3COOH is 0.200M .

Volume of HCl is 50.0mL(0.050L) .

Concentration of HCl is 1.00×103M .

The number of moles of a solute is calculated by the formula,

Molesofsolute=Volume(L)×Molarity

Substitute the value of volume and molarity of CH3COOH and HCl in the above expression.

Calculation of moles of Acetic acid and Hydrochloric acid

For CH3COOH ,

MolesofCH3COOH=0.050L×0.200M=0.01mol_

For HCl ,

MolesofHCl=0.050L×(1.00×103)M=5.0×10-5mol_

Calculation of hydrogen ion forms HCl

The total volume of the solution is calculated by the formula,

Totalvolume=VolumeofCH3COOH+VolumeofHCl

Substitute the value of the volume of CH3COOH and the volume of HCl in the above expression.

Totalvolume=(0.050+0.050)L=0.1L

HCl is a strong acid. Therefore, it completely dissociates in water. Hence, the hydrogen ion concentration is equal to the concentration of HCl .

The concentration is calculated by the formula,

Concentration=NumberofmolesVolume(L)

Substitute the value of the number of moles of HCl and the volume in the above expression.

Concentration=5.0×105mol0.10L=5.0×10-4M_

Therefore, the [H+] from HCl is 5.0×10-4M_ .

Calculation of initial concentration of Acetic acid

The concentration is calculated by the formula,

Concentration=NumberofmolesVolume(L)

Substitute the value of the number of moles of CH3COOH and the volume in the above expression.

Concentration=0.01mol0.10L=0.1M_

Therefore, the initial [CH3COOH] is 0.1M_

(a)

Interpretation Introduction

Interpretation:

A solution is made by adding 50.0 mL of 0.200M Acetic acid to 50mL of 1×10-3M HCl .

1. (a) pH of the solution is to be calculated.
2. (b) Acetate ion concentration to be calculated.

Concept introduction:

The pH of a solution is define as a figure that expresses the acidity of the alkalinity of a given solution.

The pH of a solution is calculated by the formula, pH=log[H+]

The number of moles of a solute is calculated by the formula,

Molesofsolute=Volume(L)×Molarity

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text:
# What is multi fidelity uncertainty quantification?

Uncertainty quantification (UQ) involves the quantitative characterization and management of uncertainty in a broad range of applications. It employs both computational models and observational data, together with theoretical analysis. UQ encompasses many different tasks, including uncertainty propagation, sensitivity analysis, statistical inference and model calibration, decision making under uncertainty, experimental design, and model validation. Multifidelity UQ is the use of multiple approximate models and other sources of information to accelerate the UQ task.

Multifidelity UQ methods leverage low-fidelity models to obtain computational speedups in solving UQ tasks. Rather than just replacing the high-fidelity model with a low-fidelity surrogate, multifidelity UQ methods use recourse to the high-fidelity model to establish accuracy and/or convergence guarantees on the UQ result.

Read our recent survey review paper: Peherstorfer, B., Willcox, K. and Gunzburger, M., Survey of multifidelity methods in uncertainty propagation, inference, and optimization, SIAM Review, Vol. 60, No. 3, pp. 550-591, 2018.

Our multifidelity UQ methods have three main approaches: (1) using approximate models as a control variate, (2) using approximate models as a biasing density, and (3) using old information as a source of approximate models.

Our work has developed methods for multifidelity uncertainty propagation, multifidelity failure probability estimation, multifidelity statistical inference, and multifidelity optimization under uncertainty.

## We have developed new multifidelity UQ methods that accelerate the following tasks:

Our multifidelity Monte Carlo method uses a control variate formulation to accelerate the estimation of statistics of interest using multiple low-fidelity models.

These results in the mean squared error (MSE) of the estimated mean show that MFMC achieves almost 4 orders of magnitude improvement over standard Monte Carlo simulation with high-fidelity model only.

## Multifidelity Uncertainty Propagation

Our multifidelity uncertainty propagation approach uses a control variate formulation to create the multifidelity Monte Carlo method (MFMC). The method has an optimal strategy for allocating evaluations among multiple models, so as to minimize the variance of the control variate estimator. Multi-level UQ methods (such as the multi-level Monte Carlo (MLMC) method) leverage hierarchies of models whose approximation qualities and costs are typically described with rates. Multi-level Monte Carlo uses these rates to distribute work among the models. Our multifidelity Monte Carlo method considers general low-fidelity models with properties that cannot necessarily be well described by rates.

Our multifidelity Monte Carlo method optimally allocates evaluations among multiple models, so as to minimize estimator variance.

Download our open-source multi-fidelity Monte Carlo method repo at Github: Multifidelity Monte Carlo method codes. The repo includes Matlab codes that interface easily with your analysis models to determine the optimal ordering of the models and the optimal number of model evaluations. The repo also includes a simple example that demonstrates the methods and generates plots showing the results.

## Multifidelity Global Sensitivity Analysis

Our multifidelity global sensitivity analysis (MFGSA) method expands upon the MFMC control variate approach to accelerate the computation of variance and variance-based sensitivity indices. Sensitivity indices are used to quantify and rank the relative impact of uncertainty in different inputs on the output of a system, and are usually estimated using Monte Carlo sampling. Mean estimation using N Monte Carlo samples requires N function evaluations. However, estimating sensitivity indices for d parameters requires N(d+2) samples, which can lead to a much higher cost than in Monte Carlo uncertainty propagation. Our MFGSA method achieves speed-ups that allow different uncertainties to be definitively ranked with lower computational expenditure than high-fidelity global sensitivity analysis.

These results show that with a computational budget of 2000 high-fidelity model evaluations, Monte Carlo cannot definitively rank the impact of uncertainties in the three inputs for this example because the variance of the sensitivity index estimators is so large that their ranges overlap. Our MFGSA approach achieves estimators with small enough variances so that the ranges do not overlap with the same computational budget, allowing the inputs to be ranked in order of importance. The high-fidelity Monte Carlo method would require 20000 high-fidelity evaluations to rank the inputs, so our MFGSA approach achieves a 10x speed-up.

Like our multifidelity Monte Carlo method, our MFGSA framework can use general low-fidelity models of any form and does not require the approximation quality or costs of the low-fidelity model to be described with rates. The method can distribute work among models so that the MSE of the multifidelity variance estimator is minimized.

You can download our open source MFGSA code from GitHub: Multifidelity global sensitivity analysis codes. Our code interfaces easily with your analysis models and distributes work among them to estimate sensitivity indices and the variance.

## Multifidelity Statistical Inference

Our multifidelity statistical inference approach uses a two-stage delayed acceptance Markov chain Monte Carlo (MCMC) formulation. A reduced order model is used in the first step of the two-stage MCMC method to increase the acceptance rate of candidates in the second step. In addition, the high-fidelity model outputs computed in the second step are used to adapt the reduced order model.

## Multifidelity Optimization Under Uncertainty

Our multifidelity optimization under uncertainty approach uses the control variate-based multifidelity Monte Carlo method embedded in an optimization loop. We show that the multi-fidelity information can come from a variety of information sources, including surrogate models, reduced order models, or past optimization iterations.

## Survey of multifidelity methods in uncertainty propagation, inference, and optimization

Peherstorfer, B., Willcox, K. and Gunzburger, M., SIAM Review, Vol. 60, No. 3, pp. 550-591, 2018.

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a computationally expensive high-fidelity model describes the system with the accuracy required by the current application at hand, while lower-fidelity models are less accurate but computationally cheaper than the high-fidelity model. Outer-loop applications, such as optimization, inference, and uncertainty quantification, require multiple model evaluations at many different inputs, which often leads to computational demands that exceed available resources if only the high-fidelity model is used. This work surveys multifidelity methods that accelerate the solution of outer-loop applications by combining high-fidelity and low-fidelity model evaluations. The overall premise of these multifidelity methods is that low-fidelity models are leveraged for speedup while the high-fidelity model is kept in the loop to establish accuracy and/or convergence guarantees. We categorize multifidelity methods according to three classes of strategies: adaptation, fusion, and filtering. The paper reviews multifidelity methods in the outer-loop contexts of uncertainty propagation, inference, and optimization.

[back to citation]

## Multifidelity Monte Carlo estimation of variance and sensitivity indices

Qian, E., Peherstorfer, B., O'Malley, D., Vesselinov, V. and Willcox, K., SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, Issue 2, pp. 683-706, 2018.

Variance-based sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be suffciently accurate can make these analyses intractable when the model is expensive. This work presents a multifidelity approach for estimating sensitivity indices that leverages cheaper low-fidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convection-diffusion- reaction model that demonstrate up to 10x speedups for fixed convergence levels. For the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.

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## Conditional-value-at-risk estimation via reduced-order models

Heinkenschloss, M., Kramer, B., Takhtaganov, T. and Willcox, K., SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, Issue 4, pp. 1395-1423, 2018.

This paper proposes and analyzes two reduced-order model (ROM) based approaches for the efficient and accurate evaluation of the Conditional-Value-at-Risk (CVaR) of quantities of interest (QoI) in engineering systems with uncertain parameters. CVaR is used to model objective or constraint functions in risk-averse engineering design and optimization applications under uncertainty. Evaluating the CVaR of the QoI requires sampling in the tail of the QoI distribution and typically requires many solutions of an expensive full-order model of the engineering system. Our ROM approaches substantially reduce this computational expense. Both ROM-based approaches use Monte Carlo (MC) sampling. The first approach replaces the computationally expensive full-order model by an inexpensive ROM. The resulting CVaR estimation error is proportional to the ROM error in the so-called risk region, a small region in the space of uncertain system inputs. The second approach uses a combination of full-order model and ROM evaluations via importance sampling, and is effective even if the ROM has large errors. In the importance sampling approach, ROM samples are used to estimate the risk region and to construct a biasing distribution. Few full-order model samples are then drawn from this biasing distribution. Asymptotically as the ROM error goes to zero, the importance sampling estimator reduces the variance by a factor $1-\beta \ll 1$, where $\beta \in (0,1)$ is the quantile level at which CVaR is computed. Numerical experiments on a system of semilinear convection-diffusion-reaction equations illustrate the performance of the approaches.

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## Generalized Information Reuse for Optimization Under Uncertainty with Non-Sample Average Estimators

Cook, L.W., Jarrett, J.P., and Willcox, K., International Journal for Numerical Methods in Engineering, Volume 115, Issue 12, pp. 1457-1476, 2018.

In optimization under uncertainty for engineering design, the behavior of the system outputs due to uncertain inputs needs to be quantified at each optimization iteration, but this can be computationally expensive. Multi-fidelity techniques can significantly reduce the computational cost of Monte Carlo sampling methods for quantifying the effect of uncertain inputs, but existing multi-fidelity techniques in this context apply only to Monte Carlo estimators that can be expressed as a sample average, such as estimators of statistical moments. Information reuse is a particular multi-fidelity method that treats previous optimization iterations as lower-fidelity models. This work generalizes information reuse to be applicable to quantities with non-sample average estimators. The extension makes use of bootstrapping to estimate the error of estimators and the covariance between estimators at different fidelities. Specifically, the horsetail matching metric and quantile function are considered as quantities whose estimators are not sample- averages. In an optimization under uncertainty for an acoustic horn design problem, generalized information reuse demonstrated computational savings of over 60% compared to regular Monte Carlo sampling.

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## Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation

Peherstorfer, B., Kramer, B. and Willcox, K., SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, No. 2, pp. 737-761, 2018.

Accurately estimating rare event probabilities with Monte Carlo can become costly if for each sample a computationally expensive high-fidelity model evaluation is necessary to approximate the system response. Variance reduction with importancesampling significantly reduces the number of required samples if a suitable biasing density is used. This work introduces a multifidelity approach that leverages a hierarchy of low-cost surrogate models to efficiently construct biasing densities for importance sampling. Our multifidelity approach is based on the cross-entropy method that derives a biasing density via an optimization problem. We approximate the solution of the optimization problem at each level of the surrogate-model hierarchy, reusing the densities found on the previous levels to precondition the optimization problem on the subsequent levels. With the preconditioning, an accurate approximation of the solution of the optimization problem at each level can be obtained from a few model evaluations only. In particular, at the highest level, only few evaluations of the computationally expensive high-fidelity model are necessary. Our numerical results demonstrate that our multifidelity approach achieves speedups of several orders of magnitude in a thermal and a reacting-flow example compared to the single-fidelity cross-entropy method that uses a single model alone.

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## Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models

Peherstorfer, B., Kramer, B. and Willcox, K., Journal of Computational Physics, 341:61-75, 2017.

In failure probability estimation, importance sampling constructs a biasing distribution that targets the failure event such that a small number of model evaluations is sufficient to achieve a Monte Carlo estimate of the failure probability with an acceptable accuracy; however, the construction of the biasing distribution often requires a large number of model evaluations, which can become computationally expensive. We present a mixed multifidelity importance sampling (MMFIS) approach that leverages computationally cheap but erroneous surrogate models for the construction of the biasing distribution and that uses the original high-fidelity model to guarantee unbiased estimates of the failure probability. The key property of our MMFIS estimator is that it can leverage multiple surrogate models for the construction of the biasing distribution, instead of a single surrogate model alone. We show that our MMFIS estimator has a mean-squared error that is up to a constant lower than the mean-squared errors of the corresponding estimators that uses any of the given surrogate models alone--even in settings where no information about the approximation qualities of the surrogate models is available. In particular, our MMFIS approach avoids the problem of selecting the surrogate model that leads to the estimator with the lowest mean-squared error, which is challenging if the approximation quality of the surrogate models is unknown. We demonstrate our MMFIS approach on numerical examples, where we achieve orders of magnitude speedups compared to using the high-fidelity model only.

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## Convergence analysis of multifidelity Monte Carlo estimation

Peherstorfer, B., Gunzburger, M., and Willcox, K., Numerische Mathematik, 139(3):683-707, 2018., https://doi.org/10.1007/s00211-018-0945-7.

The multifidelity Monte Carlo method provides a general framework for combining cheap low-fidelity approximations of an expensive high-fidelity model to accelerate the Monte Carlo estimation of statistics of the high-fidelity model output. In this work, we investigate the properties of multifidelity Monte Carlo estimation in the setting where a hierarchy of approximations can be constructed with known error and cost bounds. Our main result is a convergence analysis of multifidelity Monte Carlo estimation, for which we prove a bound on the costs of the multifidelity Monte Carlo estimator under assumptions on the error and cost bounds of the low-fidelity approximations. The assumptions that we make are typical in the setting of similar Monte Carlo techniques. Numerical experiments illustrate the derived bounds.

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## Optimal Model Management for Multifidelity Monte Carlo Estimation

Peherstorfer, B., Willcox, K. and Gunzburger, M. SIAM Journal of Scientific Computing, Vol. 38, No. 5, pp. A3163-A3194, 2016.

This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector machines, and simplified-physics models, does not necessarily give rise to such a hierarchy. Our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type. Instead of relying on error and cost rates, an optimization problem balances the number of model evaluations across the high-fidelity and surrogate models with respect to error and costs. We show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models. Our multifidelity method makes occasional recourse to the high-fidelity model; in doing so it provides an unbiased estimator of the statistics of the high-fidelity model, even in the absence of error bounds and error estimators for the surrogate models. Numerical experiments with linear and nonlinear examples show that speedups by orders of magnitude are obtained compared to Monte Carlo estimation that invokes a single model only.

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## Multifidelity probability estimation via fusion of estimators

Kramer, B., Marques, A., Peherstorfer, B., Villa, U. and Willcox, K., ACDL TR-2017-3, Submitted, 2017

This paper develops a multifidelity method that enables estimation of failure probabilities for expensive-to-evaluate models via a new combination of techniques, drawing from information fusion and importance sampling. We use low-fidelity models to derive biasing densities for importance sampling and then fuse the importance sampling estimators such that the fused multifidelity estimator is unbiased and has mean-squared error lower than or equal to that of any of the importance sampling estimators alone. The presented general fusion method combines multiple probability estimators with the goal of further variance reduction. By fusing all available estimators, the method circumvents the challenging problem of selecting the best biasing density and using only that density for sampling. A rigorous analysis shows that the fused estimator is optimal in the sense that it has minimal variance amongst all possible combinations of the estimators. The asymptotic behavior of the proposed method is demonstrated on a convection-diffusion-reaction PDE model for which n=1.e5 samples can be afforded. To illustrate the proposed method at scale, we consider a model of a free plane jet and quantify how uncertainties at the flow inlet propagate to a quantity of interest related to turbulent mixing. The computed fused estimator has similar root-mean-squared error to that of an importance sampling estimator using a density computed from the high-fidelity model. However, it reduces the CPU time to compute the biasing density from 2.5 months to three weeks.

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## Multifidelity Approaches for Optimization Under Uncertainty

Ng, L. and Willcox, K. International Journal for Numerical Methods in Engineering, Volume 100 Issue 10, pp. 746-772, published online 17 September, 2014, DOI: 10.1002/nme.4761.

It is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem.

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## Monte Carlo Information-Reuse Approach to Aircraft Conceptual Design Optimization Under Uncertainty

Ng, L. and Willcox, K. AIAA Journal of Aircraft, Vol. 53, No. 2, pp. 427-438, 2016.

This paper develops a multi-information source formulation for aerospace design under uncertainty problems. As a specific demonstration of the approach, it presents the optimization under uncertainty of an advanced subsonic transport aircraft developed to meet the NASA N+3 goals, and shows how the multi-information source approach enables practical turnaround time for this conceptual aircraft optimization under uncertainty problem. In the conceptual design phase, there are often uncertainties about future developments of the underlying technologies. An aircraft design that is robust to uncertainty is more likely to meet performance requirements as the technologies mature in the intermediate and detailed design phases, reducing the need for expensive redesigns. In the particular example selected here to present the new approach, the multi-information source approach uses an information-reuse estimator that takes advantage of the correlation of the aircraft model in the design space to reduce the number of model evaluations needed to achieve a given standard error in the Monte Carlo estimates of the relevant design statistics (mean and variance). Another contribution of the paper is to extend the approach to reuse information during trade studies that involve solving multiple optimization under uncertainty problems, enabling the analysis of the risk-performance trade-off in optimal aircraft designs.

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## Data-driven model reduction for the Bayesian solution of inverse problems

Cui, T., Marzouk, Y. and Willcox, K. International Journal for Numerical Methods in Engineering, Vol. 102, No. 5, pp. 966-990, published online 15 August, 2014, DOI: 10.1002/nme.4748.

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper proposes a data-driven projection-based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. First, the model reduction strategy is tailored to inverse problems: the snapshots used to construct the reduced-order model are computed adaptively from the posterior distribution. Posterior exploration and model reduction are thus pursued simultaneously. Second, to avoid repeated evaluations of the full-scale numerical model as in a standard MCMC method, we couple the full-scale model and the reduced-order model together in the MCMC algorithm. This maintains accurate inference while reducing its overall computational cost. In numerical experiments considering steady-state flow in a porous medium, the data-driven reduced-order model achieves better accuracy than a reduced-order model constructed using the classical approach. It also improves posterior sampling efficiency by several orders of magnitude compared with a standard MCMC method.

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text:
# Offset Torque Concept

Tags:
1. Mar 28, 2017

### DarkBlitz

Hello guys,

I am doing some basic design work and can't remember how offset torques work.

I am doing the sum of the torques should be equal to 0 in order to find the tipping point around either of the wheels.

My problem is with the 1000N applied at to top taking the pivot point around the left wheel.

Should I be using the component of the 1000N which is at right angles to the distance to the pivot point? (the green line) and take the green line as the distance? should I use 'h' as the distance to the pivot point with 1000N as the force? or a combination of both?

The same for m*g in the diagram. Should I assume that the centre of mass is where the weight is applied and take the perpendicular component?

Thanks very much for your help guys! Been a long time since I looked into this.

2. Mar 28, 2017

### jack action

By definition, the torque is the result of a cross product of 2 vectors, i.e. $\mathbf{T} = \mathbf{r} \times \mathbf{F}$. The magnitude of this torque (what you are looking for) is $T = rF\sin\theta$ where $\theta$ is the angle between the 2 vectors. This basically means that only the components of the vectors that are perpendicular to each other are considered.

You can see it as $r_{\perp} F$ or $r F_{\perp}$ as you wish, since both will give you the same answer: $rF\sin\theta$.

The following is a representation of $r F_{\perp}$:

The following is a representation of $r_{\perp} F$:

So in your case, you take 1000 N times h ( or $r_{\perp} F$). You could use $r F_{\perp}$ by using the length of the green line and by finding the perpendicular component of the 1000 N force (the orange line), it would give the same answer. It is just more complicated in this particular case.

Similarly, for the weight, you take mg times x2. Where x2 is the perpendicular component of the distance between the wheel and the center of mass.

3. Apr 7, 2017

### DarkBlitz

Thanks a lot! cleared it up!


text:
Tuesday, November 22, 2022

# How To Solve Velocity In Physics

## Displacement And Velocity Vectors

Basic Physics: How to Set Up AND Solve Velocity Problems
• Calculate position vectors in a multidimensional displacement problem.
• Solve for the displacement in two or three dimensions.
• Calculate the velocity vector given the position vector as a function of time.
• Calculate the average velocity in multiple dimensions.

Displacement and velocity in two or three dimensions are straightforward extensions of the one-dimensional definitions. However, now they are vector quantities, so calculations with them have to follow the rules of vector algebra, not scalar algebra.

## Example: Find Time Given Final Velocity Initial Velocity And Acceleration

A car approaching a school zone slows down from 27 m/s to 9 m/s with constant acceleration -2 m/s2.

How much time is required to slow down to final velocity?

Answer: We know initial velocity , velocity and acceleration

We first need to solve the velocity equation for time :

v = u + at

Plugging in the known values we get, t = /a t = / -2 m/s2 t = -18 m/s / -2 m/s2 t = 9 s

## Finding Initial Velocity With Final Velocity Acceleration And Timexresearch Source

• 1Know the right equation to use. In order to solve any physics problem you must know which equation to use. Writing down all of the known information is the first step to finding the right equation. If you have values for the final velocity, acceleration, and time involved, you can use the following equation:
• Initial velocity: Vi = Vf –
• Understand what each symbol stands for.
• Vi stands for initial velocity
• Vf stands for final velocity
• a stands for acceleration
• You May Like: Fsa Algebra 1 Eoc Answer Key

## How To Find Velocity And Acceleration

Example

Suppose a particle is moving along the ???x???-axis so that its position at time ???t??? is given by the formula

???s=3t^2+8t-2t^}???

Compute its velocity and acceleration as functions of ???t???. Next, decide in which direction the particle is moving when ???t=1??? and whether its velocity and speed are increasing or decreasing.

To find velocity, we take the derivative of the original position equation.

???v=s’=6t+8-5t^}???

To find acceleration, we take the derivative of the velocity function.

???a=v’=s”=6-\fract^}???

To determine the direction of the particle at ???t=1???, we plug ???1??? into the velocity function.

???v=6+8-5^}???

???v=9???

Because ???v??? is positive, we can conclude that the particle is moving in the positive direction .

To determine whether velocity is increasing or decreasing, we plug ???1??? into the acceleration function, because that will give us the rate of change of velocity, since acceleration is the derivative of velocity.

???a=6-\frac^}???

???a=-\frac???

Since acceleration is negative at ???t=1???, velocity must be decreasing at that point.

Since the velocity is positive and decreasing at ???t=1???, that means that speed is also decreasing at that point.

Starting with position, differentiate to find velocity, then differentiate again to find acceleration

## Ways To Calculate The Average Speed

Constant speed is an important concept in this formula. If an object moves at a constant speed, the formula for speed will be as under:

Speed= total distance/elapsed time

Mostly, the object travels at different speeds at a particular distance. For example, the speed of the car does not remain the same throughout the journey. It changes on the trip. There are some reasons why the speed of the car changes in the trip such as red light, speed breakers, and other obstructions on the road. These hurdles slow down the cars speed. Then the formula of the average speed of the car will be as under:

Average speed= total distance/ elapsed time

Average speed is measured in units of distance such as miles per hour, meters per second or feet per second.

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## How To Calculate Velocity

Before we explain how to calculate velocity, we’d like to note that there is a slight difference between velocity and speed. The former is determined on the difference between the final and initial position and the direction of movement, while the latter requires only the distance covered. In other words, velocity is a vector , and speed is a scalar .

It’s time to use the average velocity formula in practice. Provided an object traveled 500 meters in 3 minutes, to calculate the average velocity you should take the following steps:

• Change minutes into seconds . 3 minutes = 3 * 60 = 180 seconds,
• Divide the distance by time: velocity = 500 / 180 = 2.77 m/s.
• Let’s try another example. You want to participate in a race with your brand new car that can change its speed with an acceleration of about 6.95 m/sÂ². The competition just started. What will be your velocity after 4 seconds?

• Set initial velocity to zero, you’re not moving at the beginning of the race.
• Multiply the acceleration by time to obtain the velocity change: velocity change = 6.95 * 4 = 27.8 m/s.
• Since the initial velocity was zero, the final velocity is equal to the change of speed.
• You can convert units to km/h by multiplying the result by 3.6: 27.8 * 3.6 â 100 km/h.

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## Terminal Velocity Escape Velocity And Relativistic Velocity

Velocity is present in many aspects of physics, and we have created many calculators about it! The first velocity is the so-called terminal velocity, which is the highest velocity attainable by a free falling object. Terminal velocity occurs in fluids and depends on the fluid’s density. You can read more about it in our free fall with air resistance calculator.

Knowing how to calculate velocity is of particular importance in astrophysics since results have to be very accurate. If you’re interested in the world of massive celestial objects like suns or planets, visit our escape velocity calculator or orbital velocity calculator. You can learn a lot there!

In the high energy region, there is another important velocity – relativistic velocity. It results from the fact that no object with a non-zero mass can reach the speed of light. Why? When it approaches light speed, it’s kinetic energy becomes unattainable, very large or even infinite. You can check it with the relativistic kinetic energy calculator by filling the velocity field with the speed of light 299,792,458 m/s or 2.998e8 m/s in scientific notation. Moreover, this is a cause of other phenomena like relativistic velocity addition, time dilation, and length contraction. Also the Albert Einstein’s famous E = mc2 formula bases on the relativistic velocity concept.

## What Causes A Change In Velocity

BASIC PHYSICS: Solving 8 Velocity Problems- Guided Practice w/hardcopy

Experts depicts that forces are something that affect how objects move they may cause motion, also, they may stop, slow or even change the direction of motion of an object . As force cause changes in the speed or direction of an object, it is said to be that forces causes changes in velocity. Remember that acceleration is said to be change in velocity.

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## How To Solve For Initial Velocity And Angle

I hope you’re having a pleasant day. Wondering if I could ask for your assistance on some projectile problem in 2d plane.

How do I get the initial velocity and angle if maximum height, flight time, initial height, final height, and range are already given?

Basically I just wanted to compute for the force needed and the angle with the given parameters. The initial height or the initial elevation of the projectile, and the final height or the target elevation can be exchanged — what I mean by this is the instances where one of them is on the higher ground.

Please also note that I’m very new to interpreting math equations, a step-by-step breakdown of the solution would help me greatly. Very sorry for the trouble.

Please let me know if my question is unclear. Thank you in advance!

## Velocity Calculations Solved For Different Variables And Used In This Calculator:

Solving for the different variables we can use the following formulas:

• Given u, a and t calculate v Given initial velocity, acceleration and time calculate the velocity.
• v = u + at
• Given v, a and t calculate u Given velocity, acceleration and time calculate the initial velocity.
• u = v – at
• Given v, u and t calculate a Given velocity, initial velocity and time calculate the acceleration.
• a = /t
• Given v, u and a calculate t Given velocity, initial velocity and acceleration calculate the time.
• t = /a
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## Calculate Distance From Acceleration And Velocity

Since we are considering motion of body or object with;constant acceleration;we have an;equation of motion;which relate all these quantities.; This equation is the third equation of motion and is given by the relation

$v^2=u^2+2as$

Here,

$s$ is the distance traveled by the object in time $t$

$u$ is the;initial velocity

$v$ is the final velocity and

$a$ is the;constant acceleration;of the moving object

You can use this formula in various situations involving distance,;initial velocity,; final velocity and acceleration motion. You need to have a knowledge of three quantities to find the fourth quantity. It must be noted that this equation does not involve the time interval of motion of the object.

## How To Calculate Instantaneous Velocity

###### How to Calculate Formal Charge?

Due to the continuous motion of the objects through dimensions of space and time, it becomes imperative to calculate the instantaneous velocity. Instantaneous velocity is the mean velocity between two points on a specific path such that the time between the two points approaches zero. It is the quantity that determines the speed of an object. The speed at which an object is moving at any instant anywhere along its path. It is also known as simply velocity, which gives the velocity of an object at any whole point. Like average velocity, the instantaneous velocity is avector with a direction and magnitude.

Instantaneous refers to the time, while velocity relates to motion. These two are not compatible terms. Perhaps you mean âinfinite velocityâ or âzero velocityâ? Zero and Infinite velocities are problematic because they require a fixed absolute frame of reference in time and space, but we operate out of a relativistic frame. As such, a given object may be in a static position or stationary relative to one observer but in a moving position relative to another. Simultaneity is a relativistic idea that Changes with motion.

This article will depict the instantaneous velocity formula. Moreover, it will show you how instantaneous velocity can be calculated step by step using the base and derived physical quantities and stress on its practical applications.

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## How To Calculate Velocity With This Online Velocity Calculator:

#### Velocity :

Inputs:

• First, hit the distance covered tab
• Then, select the option for which you want to perform calculations, it can either velocity, time, or distance
• Very next, add the values into the remaining fields
• Now, all you need to make a click on the calculate button

Outputs:

The velocity finder calculates either:

• Velocity

## Finding Initial Velocity With Final Velocity Acceleration And Distance Xresearch Source

• 1Know the right equation to use. In order to solve any physics problem you must know which equation to use. Writing down all of the known information is the first step to finding the right equation. If you are given the final velocity, acceleration, and distance, you can use the following equation:
• Initial velocity: Vi =
• Understand what each symbol stands for.
• Vi stands for initial velocity
• Vf stands for final velocity
• a stands for acceleration
• d stands for distance
• 2Fill in the known information. Once you have written the known information and determined the proper equation, you can fill in values for the appropriate variables. Carefully setting up each problem and writing out every step of the process is important.
• If you make a mistake, you can easily find it by looking back at all of your previous steps.
• 3Solve the equation. With all of the numbers in place, use the proper order of operations to finish the problem. If youre allowed, use a calculator to limit the number of simple math mistakes.
• For example: An object accelerating north at 5 meters per second squared traveled 10 meters , ending up at a final velocity of 12 meters per second. Calculate the object’s initial velocity.
• Write the known information:
• Vi =;?, Vf = 12 m/s, a = 5 m/s2, d = 10 m
• Square the final velocity. Vf2= 122 = 144
• Multiply the acceleration by the distance and the number two. 2 * a * d = 2 * 5 * 10 = 100
• Subtract this product from your previous one. Vf2 – = 144 100 = 44
• You May Like: Eoc Fsa Warm Ups Algebra 1 Answers

## Best Ways To Learn Physics Easily

If you are finding Physics a bit tough, you can try these methods to learn effectively.

#### Gaining mastery in basic concepts

To be an expert in this subject, you have to remember all the basic physics formulas properly. You should be master in knowing the Central theories of physics. These theories will make it simpler for you to solve even the mathematical problems. Central theories are also used in the physical world to a large extent.

Math is directly related to physics. There are some mathematical problems which you need to learn to further learn physics more perfectly. You have to gain expertise in the equation for velocity and other formulas. You can learn math and physics simultaneously for better understanding.

#### Remember basic equations

Physics basically describes the relationship between speed, velocity, force, and acceleration. With these concepts, you can solve every easy or difficult problem of physics. You have to memorize the average speed formula and velocity formula for solving the problems. Learning basic equations will make the subject easier and simpler for you.

#### Derivations

While solving the problems of physics, it is important to understand the working of it. You should go through each step of the problem and understand how it is derived. Here, you should be well versed again with the basic equations of physics.

## The Concept Is Related To Distance Rate And Time

How to Calculate Velocity
• M.S., Mathematics Education, Indiana University
• B.A., Physics, Wabash College

Velocity is defined as a vector measurement of the rate and direction of motion. Put simply, velocity is the speed at which something moves in one direction. The speed of a car traveling north on a major freeway and the speed a rocket launching into space can both be measured using velocity.

As you might have guessed, the scalar magnitude of the velocity vector is the speed of motion. In calculus terms, velocity is the first derivative of position with respect to time. You can calculate velocity by using a simple formula that includes rate, distance, and time.

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## Interesting Facts About Speed And Velocity:

• Galileo Galilei was the first scientist who measures speed as distance over time
• A speedometer is said to be the best example of instantaneous speed
• You can also express a speed of light as 186,282 miles per second
• The speed of sound in dry air can be expressed as 343.2 meters per second
• The escape velocity of Earth is referred to as the speed that needed to escape from Earths gravitational pull. It is expressed as 25,000 miles per hour

## How Long Does It Take To Reach Terminal Velocity

It will take the average human approximately 15 seconds to reach 99% of terminal velocity with their belly facing the Earth. Reach 100% terminal velocity is very difficult, if not impossible, as acceleration drops exponentially as an object approaches its terminal velocity. This time will change if the personâs changes body position.

## Speed Velocity And Acceleration

Speed, velocity, and acceleration are all related to each other, though they represent different measurements. Be careful not to confuse these values with each other.

• Speed, according to its technical definition,;is a scalar quantity that indicates the rate of motion distance per time. Its units are length and time. Put another way, speed is a measure of;distance;traveled over a certain amount of time. Speed is often described simply as;the distance traveled per unit of time. It is how fast an object is moving.;
• Velocity;is a vector quantity that indicates displacement, time, and direction. Unlike speed, velocity measures displacement, a vector quantity indicating the difference between an object’s final and initial positions. Speed measures distance, a scalar quantity that measures the total length of an object’s path.
• Acceleration;is defined as a vector quantity that indicates the rate of change of velocity. It has dimensions of length and time over time. Acceleration is often referred to as “speeding up”, but it really measures changes in velocity. Acceleration can be experienced every day in a vehicle. You step on the accelerator and the car speeds up, increasing its velocity.

## Find The Equation Of Motion

To be able to compute the velocity of an object at any instant, its equation of motion needs to be figured out.

Velocity is a vector quantity, thats formally defined as the rate of change of position or displacement with time. When stating any vector like the velocity of an object, we talk about direction, as well as magnitude. Thats why, speed and velocity are different things. Speed is a scalar , while velocity is a vector. To put it simply, speed is the magnitude of velocity. When talking about velocity, we specify it according to some fixed frame of reference and its unit is meters/second. It can be measured in two ways. One is in the form of average velocity, while the other is instantaneous velocity. The formula for the former is as follows.

Average Velocity = S/T

Here, S is the distance covered and T is the time period of travel.

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