I'm wondering about how one would describe the dynamics of a rotating sphere. Consider this: a solid sphere of mass "m" and radius "r" is set to rotate about a tangent to its surface. If it is released from the horizontal position such that it swings like a pendulum, what would be the force acting on the sphere at the lowest point (force from pivot, i.e. centripetal force) First of all, one could find the moment of inertia using the parallel axis theorem correct? So I = Icm + mr² I = (7/5)mr² Now we could say that its being released from a height "h" of h = 2r So the potential energy is converted to rotational kinetic energy: mgh = ½Iω² mgh = ½((7/5)mr²)ω² gh = (7/10)r²ω² Now I'm puzzled, the force acts on the body's center of mass or the surface? Could we replace ωr = v to find the velocity about the center of mass and use that velocity to find the centripetal force? I.e.; v² = (10/7)gh And F - mg = mv²/r F = mv²/r + mg F = m(v²/r + g) F = m((10/7)gh/r + g) F = mg((10/7)h/r + 1) This makes sense right? Since the velocity at the center of mass of the sphere is simply v = rω where r is the radius of the circular path of rotation, which happens to be the radius of the sphere? I need some help with this, thanks!