Important questions of system of particles and rotational motion
In this assignment we are providing for the students, Important questions of system of particles and rotational motion . Students who is already completed the theory and derivation of entire chapter should solve all the questions given in this assignment ” Important questions of system of particles and rotational motion”. Since numbers of questions in this assignment is very less, so it can be revised or solved in very short time .
System of particle and rotational motion
- Is it possible to open a pen cap with one finger? Why?
- When a sphere, ring, disc and spherical shell are coming down on an inclined plane, rolling without slipping, which will reach the ground first?
- How will you distinguish between a hard-boiled egg and a raw egg by spinning each on a table top?
- Find the torque of a force 7î-3jˆ-5kˆ about the origin which acts on a particle whose position vector is iˆ+jˆ-kˆ.
- What is torque? Write its formula in vector form. Handle, to open the door, is always provided at the free edge of a door. Why?
- Establish the relation between angular momentum and rotational kinetic energy?
- If earth were to shrink suddenly, what would happen to the length of the day?
- Derive the relations
- L = I ω (ii) Ʈ = Iα
- If angular momentum is covered in a system whose moment of inertia is decreased, will its rotational kinetic energy to be also conserved? Explain.
- Can a body in translatory motion have angular momentum? Explain.
- A ring, a dice and a sphere all of the same radius and same mass roll down on an inclined plane from the same height h. Which of the three reaches the bottom
(i)earliest (ii) latest ?
- Write an expression for the moment of inertia of a circular disc of a mass M and radius R
(i)about an axis passing through its center, and a perpendicular to its plane.
(ii) about its diameter.
(iii)about a tangent to its own plane.
(iv) about a tangent perpendicular to the plane of the disc.
- How much fraction of the K.E. of rolling is purely (i) translational (ii) rotational ?
- Obtain an expression for position vector of center of mass of a two particle system.
- What is the difference between rotational kinetic energy and rolling kinetic energy?
Show that rolling kinetic energy of a rolling body is given by 1/2mv2(( K2/r2)+1) , where r is the radius of the body and K is the radius of gyration of the body.
- (i) Define moment of inertia. Write the parallel and perpendicular axis theorem.
- Derive an expression for moment of inertia of a disc of radius r, mass m
- Prove that the rate of a change of the angular momentum of particle is equal the torque of acting on it.
- Define moment inertia. Write any two factors which it depends. When the diver leaves the diving board, why does he bring his hand and feet closer together in order to make a some result ?
- Derive an expression for moment of inertia of a thin circular ring passing through the centerrotational motionr and perpendicular to the plane of the ring.
- (I)Define moment of inertia .write the parallel and perpendicular axis theorem .(II)derive an expression for moment of inertia of a disc of radius r , mass m about the axis along its diameter.
- A rope of negligible mass is wound round a hollow cylinder of mass 3kg and radius 40cm . what is the angular acceleration of the cylinder if the rope is pulled by a force of 30N?what is the linear acceleration of the rope?
- From a uniform circular disc of diameter d , a circular hole of diameter d/6 and having its center at a distance of d/4 from the center of the disc is scooped out , find the center of mass of the remaining portion .
- A uniform ring of mass 10kg and diameter 0.40m rotate with the uniform speed of 2100 rpm, find the moment of inertia and angular momentum of the ring about its geometric axis
- A cylinder of mass 5kg and radius 30cm and free to rotate about its axis , receive an angular impulse of 3kg m2/s followed by a similar impulse after every 4 sec . what is the angular speed of the cylinder 30 sec. after the initial impulse ? the cylinder is at rest initially.
- Two particles of mass 2kg and 1kg are moving along the same line with speeds 2m/s and 5m/s respectively . what is the speed of the center of mass of the system if both the particles are moving (a) in the same direction (b) in opposite direction ?