**Goal:** Problem solving with dynamics

**Source:** UMPERG-ctqpe168

A

uniform disk with mass M and radius R rolls without slipping down an

incline 30° to the horizontal. The friction force acting through

the contact point is

- 0
- Mg/3
- Mg/4
- Mg/6
- none of the above

## Commentary:

## Answer

(4) This problem requires students to use the 2nd law written in

terms of the CM acceleration and the rotational dynamic relation written

about the CM or the contact point. In either case they also need the

geometric constraint for rolling. This is a difficult problem for

students requiring a lot of additional knowledge, such as the moment of

inertia for a disk and, depending upon solution method, the Parallel

Axis Theorem.

Having gone to the trouble of solving the problem it is best to make

sure that the students glean as much as they can. A good followup

question is which would have a larger friction force, a hoop, a disk or

a sphere. They may try to reason from the acceleration of these objects

that the larger the acceleration, the smaller the friction force. The

friction force depends upon the mass, however, and the question cannot

be answered without knowledge of the masses.