Presentation on theme: "11.4 Tangent Vectors and Normal Vectors Find a unit tangent vector at a point on a space curve Find the tangential and normal components of acceleration."— Presentation transcript:
11.4 Tangent Vectors and Normal Vectors Find a unit tangent vector at a point on a space curve Find the tangential and normal components of acceleration
11.5 Arc Length and Curvature Find arc length of a space curve Arc length parameter to describe plane curves/space curves Curvature of a curve at a point on the curve Use vector-valued functions to find frictional force.
Acceleration, speed, and curvature pg.826 Normal component of acceleration – Function of BOTH speed and curvature – Measures acceleration acting perpendicular to direction of motion – Ex. Driving car around a turn Tangential component of acceleration=rate of change of the speed – Negative when object slows down – Positive when speeds up – Solely a function of the arc length
Frictional Force pg. 827 A 360 kg go-cart is driven at a speed of 60 km/hr around a circular racetrack of radius 12 meters. To keep the cart from skidding off course, what frictional force must the track surface exert on the tires?
PG. 828 # 1, 3, 7, 9 (DO NOT DRAW), 15, 17, 21-29 ODD, 37, 39, 51 Homework for Section 11.5