# Rotating cylinder against rough walls

A uniform cylinder of radius $$R$$ is rotated about an axis passing through its center, with an angular velocity of $$\omega$$. It's then placed on the floor and against the wall. Both the wall and the floor have the coefficient of friction $$k$$.

If the number of rotations accomplished by the cylinder before coming to rest can be expressed as $\frac{(w^a)R(1+\big(k^b)\big)}{c(\pi)(k^d)\big(1+(k^e)\big)g},$ where $$a,b,c,d,e$$ are positive integers and $$g$$ is the acceleration due to gravity, find $$a+b+c+d+e$$.

×