Chapter 8, Problem 48P

A solid uniform sphere of mass m and radius R rolls without slipping down an incline of height h. (a) What forms of mechanical energy are associated with the sphere at any point along the incline when its angular speed is ω? Answer in words and symbolically in terms of the quantities m, g, y, I, ω, and v. (b) What force acting on the sphere causes it to roll rather than slip down the incline? (c) Determine the ratio of the sphere’s rotational kinetic energy to its total kinetic energy at any instant.