Q11. Rotational Vectors, Angular Momentum

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: zero 27 m 13.5 m 18 m none of these <PowerClick><Answer>3</Answer><Option>5</Option></PowerClick>

half its translational kinetic energy A hoop rolls with constant velocity and without sliding along level ground. Its rotation kinetic energy is: half its translational kinetic energy the same as its translational kinetic energy twice its translational kinetic energy four times its translational kinetic energy one-third its translational kinetic energy <PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

half its translational kinetic energy the same as its translational kinetic energy twice its translational kinetic energy four times its translational kinetic energy one-third its translational kinetic energy

moves to the left and rotates counterclockwise A yo-yo, arranged as shown, rests on a frictionless surface. When a force is applied to the string as shown, the yo-yo: moves to the left and rotates counterclockwise moves to the right and rotates counterclockwise moves to the left and rotates clockwise moves to the right and rotates clockwise moves to the right and does not rotate <PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

1. F makes CM move to the right. 2. Torque wrt CM  CCW rotation about CM.

A 2. 0-kg block starts from rest on the positive x axis 3 A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by a  4.0 i  3.0 j in m/s2. At the end of 2.0 s its angular momentum about the origin is: ( –36 kgm2/s ) k ( +48 kgm2/s ) k ( –96 kgm2/s ) k ( +96 kgm2/s ) k <PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

r0 = (3,0) a = (4,3) r v L At 2s,

A 2.0-kg stone is tied to a 0.50 m long string and swung around a circle at a constant angular velocity of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The magnitude of the torque about the origin is: 6.0 N  m 14 N  m 72 N  m 108 N  m <PowerClick><Answer>5</Answer><Option>5</Option></PowerClick>

 = 12 rad/s F 2 kg 0.5 m  r 0.75 m

Motorized Gyroscope: Up Down To the left To the right Movie Up Down To the left To the right None of the above <PowerClick><Answer>1</Answer><Option>5</Option></PowerClick>

F F     r   L // r  r , L Movie_Ans F      L , r 

Satellite Derotator: Stops Spins CCW (forward) Spins CW (backward) Movie Stops Spins CCW (forward) Spins CW (backward) <PowerClick><Answer>3</Answer><Option>5</Option></PowerClick>

V , m r R m, V Starting from rest :  Same   same L 