**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?