Rotational Motion Practice Problems for AP Physics B & C

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By — McGraw-Hill Professional
Updated on Feb 11, 2011

Review the following concepts if necessary:


Multiple Choice:

  1. All of the objects mentioned in the choices below have the same total mass and length. Which has the greatest moment of inertia about its midpoint?
    1. a very light rod with heavy balls attached at either end
    2. a uniform rod
    3. a nonuniform rod, with the linear density increasing from one end to the other
    4. a nonuniform rod, with the linear density increasing from the middle to the ends
    5. a very light rod with heavy balls attached near the midpoint
  2. A pool ball is struck at one end of the table; it moves at constant speed to the far end of the table. A camera is mounted at the side pocket at the table's midpoint, as shown. From the camera's point of view, the pool ball travels from right to left. At which point in its motion does the ball have the greatest angular momentum about the camera's position?
    1. when the ball was first struck
    2. at the midpoint of the table
    3. the angular momentum is the same throughout the motion
    4. at the far end of the table
    5. one quarter of the way across the table, and then again 3/4 of the way across the table
  3. A ladder of length L leans against a wall at an angle of θ from the horizontal, as shown above. The normal force FN applied from the ground on the ladder applies what torque about the ladder's center of mass?
    1. FN · (L/2)
    2. FN · L cos θ
    3. FN · L sin θ
    4. FN · (L/2) cos θ
    5. FN · (L/2) sin θ
  4. The front wheel on an ancient bicycle has radius 0.5 m. It moves with angular velocity given by the function w(t) = 2 + 4t2, where t is in seconds. About how far does the bicycle move between t = 2 and t = 3 seconds?
    1. 36 m
    2. 27 m
    3. 21 m
    4. 14 m
    5. 7 m

Free Response:

  1. (This one's tough!) A stick of mass M and length L is pivoted at one end. A small mass m << M is attached to the right-hand end of the stick. The stick is held horizontally and released from rest.
    1. Given that the moment of inertia of a uniform rod pivoted around one end is (1/3)ML2, determine the moment of inertia of the described contraption.
    2. Calculate the angular velocity of the contraption when it reaches a vertical position.
    3. Calculate the linear velocity of the small mass m when it is at its lowest position.
    4. The figure below represents the stick at its lowest position. On this figure, draw a vector to represent the net force on the rod's center of mass at this point. Justify your answer.
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