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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/s 2 . The distance traveled by the center of the wheel from t = 0 to t = 3 s is:.
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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
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
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
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
r 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 3.0 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: • 0 • ( –36 kgm2/s ) k • ( +48 kgm2/s ) k • ( –96 kgm2/s ) k • ( +96 kgm2/s ) k
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: • 0 • 6.0 N m • 14 N m • 72 N m • 108 N m
= 12 rad/s F 2 kg 0.5 m r 0.75 m
Motorized Gyroscope: Movie • Up • Down • To the left • To the right • None of the above
F F r L // r r , L Movie_Ans F L , r
Satellite Derotator: Movie Stops Spins CCW (forward) Spins CW (backward)
V , m r R m, V Starting from rest : Same same L