Explain why a uniform solid cylinder and a uniform hollow cylinder of the same mass and outer radius, released simultaneously from rest at the top of an inclined plane, reach the bottom at different times, even though no energy is lost to friction that causes slipping.

A uniform solid cylinder and a uniform hollow cylinder of the same mass and outer radius, when released from rest on an incline, both roll without slipping. The gravitational potential energy lost is converted into translational kinetic energy frac12mv^2 and rotational kinetic energy frac12Iomega^2, with omega=v/r. For a given mass and radius the hollow cylinder has a larger moment of inertia I_hollow> I_solid because its mass is farther from the axis. Thus, for the same linear speed v, a larger fraction of the energy is stored as rotational kinetic energy in the hollow cylinder, leaving less energy for translational motion. Consequently the hollow cylinder has a smaller linear acceleration down the slope and reaches the bottom later than the solid cylinder.