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Formative assessment questions for teaching physics

A2L Item 188

  • Description: Determine the acceleration of a disk rolling down an incline.
  • Goal: Problem solving with rotational dynamics
  • Source: UMPERG-ctqpe167
  • Keywords: Acceleration, Mechanics, Rotational Dynamics

The question for students:

Item188_fig1.gif A uniform disk with mass M and radius R rolls without slipping down an incline 30° to the horizontal. The acceleration of the center of the disk is

  1. g/2
  2. 2g/3
  3. 3g/4
  4. g/4
  5. none of the above

Commentary for teachers:

Answer

(5) The acceleration must be smaller than for a mass sliding on a frictionless incline, but larger than for a hoop. Application of the rotational dynamic relation τ = Ipαp about point P, the disk’s contact point with the incline yields an acceleration of g/3. Students must know the moment of inertia of the disk about its center and use the Parallel Axis Theorem.

Good discussion questions are: Would a marble have a larger or smaller acceleration than a coin? Would the angle of the incline matter?