Application of force not acting through center of mass.

1. Oct 7, 2012

Hello PF!

I've got a lab on rigid body motion tomorrow, and I need help completing one of the prep questions:

A rigid body is acted on by a force F through its center of mass, and also experiences a torque caused by a similar force F at radius R. At time t, what are the linear and angular velocities of the rigid body? Show that they follow the relationship:

v = $\frac{1}{2}$ ω R

I understand that there is a translational as well as a rotational component to the F applied at radius R, but I'm not sure how to combine them.

I'm also unclear on whether the radius R is the radius of the body, or just the radius at which the second force is applied. But there was a previous question where R was defined as the radius of a uniform disc, so I'm leaning towards the former.

Thanks!