Question

Two forces `F_1` and `F_2` are applied on a spool of mass M and moment of inertia I about an axis passing through its center of mass. Find the ratio `F_1/F_2`, so that the force of friction is zero. Given that `I<2MR^2`?

Answer 1

See below.

Explanation:

Friction force `f` depends only on normal force

`N = M g rArr f = mu N = mu M g`

The movement equation regarding the spool center

`I dot omega = R F_2-2R F_1-2Rf`

then making

`RF_2 = 2R f rArr F_2 = 2mu M g` the friction force is cancelled.