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:
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
- g/2
- 2g/3
- 3g/4
- g/4
- 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?