Consider a lollipop made of a solid sphere of mass m and radius r that is radially pierced by a massless stick. The free end of the stick is pivoted on the ground, which is frictionless. The sphere slides along the ground, with the same point on the sphere always touching the ground. The center moves in a circle of radius R with frequency Ω. Show that the normal force between the ground and the sphere is N = mg + mrΩ^2, which is independent of R. Solve this by:
a) Using an F = ma argument.
b) Using the more complicated torque = dL/dt argument.