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Formative assessment questions for teaching physics

A2L Item 187

  • Description: Determine the acceleration of a rolling disk pulled by a string wrapped about its circumference.
  • Goal: Problem solving
  • Source: UMPERG-ctqpe160
  • Keywords: Acceleration, Forces, Mechanics, Rotational Dynamics

The question for students:

Item187_fig1.gif A uniform disk with R=0.2m rolls without slipping on a horizontal surface. String is pulled in the horizontal direction with force 15N. Moment of inertia of disk is 0.4 kg-m2. The acceleration of the center of the disk is most nearly

  1. 0.5 m/s2
  2. 1 m/s2
  3. 4 m/s2
  4. 7.5 m/s2
  5. 10 m/s2
  6. none of the above

Commentary for teachers:

Answer

(2) This problem can be done without knowing anything about the friction force. To do so, though, requires knowing the Parallel Axis Theorem for moments of inertia and the constraint between the linear and rotational rates of motion for a rolling object. An alternate method is to write the two equations for the linear motion of the center of mass and the torque relation for rotation about the CM and then eliminate the friction from the two equations.