A hollow cylinder with a very thin wall (like a toilet paper tube) and a block are placed at rest at the top of a plane with inclination θ above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found that both objects reach the bottom of the plane simultaneously. What is the coeﬃcient of kinetic friction between the block and the plane?
Iα = τ
The Attempt at a Solution
So for this problem, I figured that their accelerations had to be equal. The blog's acceleration was simply
gsinθ - μgcosθ
However, I'm having trouble finding the cylinder's acceleration.
Iα = τ
Summing torque around the point of contact of the cylinder (to eliminate normal force as producing a torque) I have that
τ = mgr sin θ = Iα
However, I'm not sure how to get the moment of inertia. As it's not around the Center of mass, it's not going to be MR2 for this particular reference point. Could anyone help me out here? How do I solve this problem using the COM as a reference point?