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 \(a+b+c+d+e\).

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