A ring and a disc having masses in the ratio 1:2 are made to rotate about their central axes. Both are acted upon by the same torque when they are at rest. Which one will have more angular velocity when torque has been removed from both after the same time? Both have the same radius.

Depends on ratio of mass and radius

A hollow rod has frictionless inner walls. Inside the rod are two small spheres that are kept on either side of the centre of rod. The rod is rotated about its central axis which is perpendicular to the plane of rotation. If the rod had been rotated by an impulsive torque which gave it an instantaneous angular velocity of 5rad/s, what will be the angular velocity after some finite but long time t ? Assume no external forces act on rod after the impulse. Also state what will happen to the spheres in the centre of the rod. The rod has a mass =2kg & length =10cm. The two spheres have a mass =1kg each.

2.5 rad/s, spheres will move to opposite ends of rod

2.5 rad/s, spheres will stay where they are as there is no friction to move them

0 rad/s, spheres will move outwards and decrease velocity of rod to zero

1.25 rad/s, spheres will move to opposite ends of rod

2.5 rad/s, spheres will move to opposite ends of rod

Can t conserve angular momentum because of friction

Angular momentum of the particle

Change in kinetic energy of the particle

Rate of change of angular momentum

1.	A ring and a disc having masses in the ratio 1:2 are made to rotate about their central axes. Both are acted upon by the same torque when they are at rest. Which one will have more angular velocity when torque has been removed from both after the same time? Both have the same radius.
A.	Ring
B.	Disc
C.	Same for both
D.	Depends on ratio of mass and radius
Answer» D. Depends on ratio of mass and radius

2.	A hollow rod has frictionless inner walls. Inside the rod are two small spheres that are kept on either side of the centre of rod. The rod is rotated about its central axis which is perpendicular to the plane of rotation. If the rod had been rotated by an impulsive torque which gave it an instantaneous angular velocity of 5rad/s, what will be the angular velocity after some finite but long time t ? Assume no external forces act on rod after the impulse. Also state what will happen to the spheres in the centre of the rod. The rod has a mass =2kg & length =10cm. The two spheres have a mass =1kg each.
A.	2.5 rad/s, spheres will stay where they are as there is no friction to move them
B.	0 rad/s, spheres will move outwards and decrease velocity of rod to zero
C.	1.25 rad/s, spheres will move to opposite ends of rod
D.	2.5 rad/s, spheres will move to opposite ends of rod
Answer» D. 2.5 rad/s, spheres will move to opposite ends of rod

3.	A disc is rotating with =10rad/s about a fixed central axis which is perpendicular to its plane. The disc has a mass =2kg & radius =10cm. A small particle of mass 100gm is put slowly on the disc s outer circumference. There is sufficient friction between the disc and the particle. What will be the new angular velocity of the system?
A.	10 rad/s
B.	9.09 rad/s
C.	9.51 rad/s
D.	Can t conserve angular momentum because of friction
Answer» C. 9.51 rad/s

4.	A particle of mass 5kg is rotating about an axis in a circle with a speed of 10m/s. What should be its radius so that the component of angular momentum about the axis is 5kgm²/s?
A.	0.1cm
B.	10cm
C.	5cm
D.	0.5m
Answer» C. 5cm

5.	Which of the following quantities is zero if torque on a particle is zero?
A.	Angular momentum of the particle
B.	Angular speed of the particle
C.	Change in kinetic energy of the particle
D.	Rate of change of angular momentum
Answer» E.

6.	What is the rate of change of angular momentum?
A.	Force
B.	Torque
C.	Work
D.	Angular velocity
Answer» C. Work

7.	The angular momentum vector of a particle about a point on the rotational axis is parallel to its angular velocity vector, provided the particle rotates with fixed speed about that axis. True or False?
A.	True
B.	False
Answer» C.

8.	A particle is rotating about a fixed axis. The angular momentum of the particle about any point on the fixed axis is the same. True or False?
A.	True
B.	False
Answer» C.