# Rolling, Torque and Angular Momentum - Chapter No 10

Right Answers have been shown below in red color.

1. A wheel rolls without sliding along a horizontal road as shown. The velocity of the center of the wheel is represented by →. Point P is painted on the rim of the wheel. The instantaneous velocity of point P is:

A. →
B. ←
C. ↑
D. ↓
E. zero

2. A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s2. The distance traveled by
the center of the wheel from t = 0 to t = 3 s is:

A. zero
B. 27 m
C. 13.5 m
D. 18 m
E. none of these

3. Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is twice the radius of wheel 1. The angular velocity of wheel 2 is:

A. twice the angular velocity of wheel 1
B. the same as the angular velocity of wheel 1
C. half the angular velocity of wheel 1
D. more than twice the angular velocity of wheel 1
E. less than half the angular velocity of wheel 1

4. A forward force on the axle accelerates a rolling wheel on a horizontal surface. If the wheel does not slide the frictional force of the surface on the wheel is:

A. zero
B. in the forward direction
C. in the backward direction
D. in the upward direction
E. in the downward direction

5. When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is:

A. forward for all tires
B. backward for all tires
C. forward for the front tires and backward for the rear tires
D. backward for the front tires and forward for the rear tires
E. zero

5. When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is:

A. forward for all tires
B. backward for all tires
C. forward for the front tires and backward for the rear tires
D. backward for the front tires and forward for the rear tires
E. zero

6. A solid wheel with mass M, radius R, and rotational inertia MR2/2, rolls without sliding on a horizontal surface. A horizontal force F is applied to the axle and the center of mass has an
acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

A. F = M a, f = 0
B. F = M a, f = M a/2
C. F = 2M a, f = M a
D. F = 2M a, f = M a/2
E. F = 3M a/2, f = M a/2

7. The coefficient of static friction between a certain cylinder and a horizontal floor is 0.40. If the rotational inertia of the cylinder about its symmetry axis is given by I = (1/2)MR2, then the magnitude of the maximum acceleration the cylinder can have without sliding is:

A. 0.1g
B. 0.2g
C. 0.4g
D. 0.8g
E. g

8. A thin-walled hollow tube rolls without sliding along the floor. The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass) is:

A. 1
B. 2
C. 3
D. 1/2
E. 1/3

9. A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane and roll without sliding down the incline. Then:

A. the sphere reaches the bottom first because it has the greater inertia
B. the cylinder reaches the bottom first because it picks up more rotational energy
C. the sphere reaches the bottom first because it picks up more rotational energy
D. they reach the bottom together
E. none of the above are true

10. A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines. Rank the objects according to how high they go, least to greatest.

A. hoop, disk, sphere
B. disk, hoop, sphere
C. sphere, hoop, disk
D. sphere, disk, hoop
E. hoop, sphere, disk

11. A hoop rolls with constant velocity and without sliding along level ground. Its rotational kinetic energy is:

A. half its translational kinetic energy
B. the same as its translational kinetic energy
C. twice its translational kinetic energy
D. four times its translational kinetic energy
E. one-third its translational kinetic energy

12. Two identical disks, with rotational inertia I (= 1/2MR2), roll without sliding across a horizontal floor with the same speed and then up inclines. Disk A rolls up its incline without sliding. On the other hand, disk B rolls up a frictionless incline. Otherwise the inclines are identical. Disk A reaches a height 12 cm above the floor before rolling down again. Disk B reaches a height above the floor of:

A. 24 cm
B. 18 cm
C. 12 cm
D. 8 cm
E. 6 cm

13. A yo-yo, arranged as shown, rests on a frictionless surface. When a force F is applied to the string as shown, the yo-yo:

A. moves to the left and rotates counterclockwise
B. moves to the right and rotates counterclockwise
C. moves to the left and rotates clockwise
D. moves to the right and rotates clockwise
E. moves to the right and does not rotate

14. When we apply the energy conservation principle to a cylinder rolling down an incline without sliding, we exclude the work done by friction because:

A. there is no friction present
B. the angular velocity of the center of mass about the point of contact is zero
C. the coefficient of kinetic friction is zero
D. the linear velocity of the point of contact (relative to the inclined surface) is zero
E. the coefficient of static and kinetic friction are equal

15. Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is:

A. the one with the larger mass
B. the one with the smaller mass
C. the one with the larger rotational inertia
D. the one with the smaller rotational inertia
E. neither (they arrive together)

16. A 5.0-kg ball rolls without sliding from rest down an inclined plane. A 4.0-kg block, mounted on roller bearings totaling 100 g, rolls from rest down the same plane. At the bottom, the block
has:

A. greater speed than the ball
B. less speed than the ball
C. the same speed as the ball
D. greater or less speed than the ball, depending on the angle of inclination
E. greater or less speed than the ball, depending on the radius of the ball

17. A cylinder of radius R = 6.0 cm is on a rough horizontal surface. The coefficient of kinetic friction between the cylinder and the surface is 0.30 and the rotational inertia for rotation
about the axis is given by MR2/2, where M is its mass. Initially it is not rotating but its center of mass has a speed of 7.0 m/s. After 2.0 s the speed of its center of mass and its angular velocity about its center of mass, respectively, are:

A. 1.1 m/s, 0

18. The fundamental dimensions of angular momentum are:

A. mass·length·time−1
B. mass·length−2·time−2
C. mass2·time−1
D. mass·length2·time−2
E. none of these

19. Possible units of angular momentum are:

A. kg·m/s
B. kg·m2/s2
C. kg·m/s2
D. kg·m2/s
E. none of these

20. The unit kg·m2/s can be used for:

A. angular momentum
B. rotational kinetic energy
C. rotational inertia
D. torque
E. power