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#?

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Answer 1 · 2018-03-13T12:17:29

See below.

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.