A uniform hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. The only external force is that of gravity. If the smaller cylinder starts rolling from rest on top of the bigger cylinder , use the method of lagrange multipliers to find the point at which the hoop falls off the cylinder.
The Attempt at a Solution
So, it will fall off when the radial force is 0, right? Should I use virtual forces and d'Alemberts principle to do this problem? I want to get the radial force as a function of the angle that the smaller hoop rotates along the cylinder, right?
EDIT: the word smaller in the last sentence should not be there because there is only one hoop