Q. A disk has mass m and outer radius R with a radial mass distribution (which can not be uniform) so that its moment of inertia is 3 mR2. The disk is given a hard kick 8 (impulse) along a horizontal surface at time t0. The kicking force acts along a horizontal line through the disk's center, so the disk acquires a linear velocity v0 but no initial angular velocity. The coefficient of friction between disk and surface is μ.

The kinetic friction force between surface and disk slows down its linear motion while at the same time making the disk spin on its axis at an accelerating rate. Finally, the disk's rotation catches up with its linear motion, and disk begins to roll at time trolling without slipping on the surface.