A2L Item 189
- Description: Determine the friction force acting on a disk rolling down an incline.
- Goal: Problem solving with dynamics
- Source: UMPERG-ctqpe168
- Keywords: Forces, Friction, Mechanics, Rotational Motion
The question for students:
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 for teachers:
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.