**Goal:** Problem solving

**Source:** UMPERG-ctqpe160

A

uniform disk with R=0.2m rolls without slipping on a horizontal surface.

String is pulled in the horizontal direction with force 15N. Moment of

inertia of disk is 0.4 kg-m^{2}. The acceleration of the center

of the disk is most nearly

- 0.5 m/s
^{2} - 1 m/s
^{2} - 4 m/s
^{2} - 7.5 m/s
^{2} - 10 m/s
^{2} - none of the above

## Commentary:

## Answer

(2) This problem can be done without knowing anything about the

friction force. To do so, though, requires knowing the Parallel Axis

Theorem for moments of inertia and the constraint between the linear and

rotational rates of motion for a rolling object. An alternate method is

to write the two equations for the linear motion of the center of mass

and the torque relation for rotation about the CM and then eliminate the

friction from the two equations.