# 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.

> IB DP Physics Higher Level (2023 syllabus) — A.4 Rigid body mechanics (HL only) · Explain · 4 marks

## Mark scheme (4 marks)

1. Rolling without slipping converts gravitational potential energy into both translational kinetic energy and rotational kinetic energy.
2. The hollow cylinder has a greater moment of inertia than the solid cylinder (for the same mass and outer radius) because more of its mass is distributed farther from the rotational axis.
3. For a given linear speed, a greater moment of inertia means more energy is stored as rotational kinetic energy, so less energy is available for translational kinetic energy.
4. Therefore the hollow cylinder has a lower translational (linear) acceleration down the slope and arrives at the bottom after the solid cylinder.

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