Goal: Problem solving with rotational dynamics
Source: UMPERG-ctqpe167
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:
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?