Two rigid objects roll without slipping across a horizontal surface: object A is a…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
Two rigid objects roll without slipping across a horizontal surface: object A is a solid uniform cylinder of mass M and radius R, while object B is a solid uniform sphere of the same mass and radius. Both objects possess exactly the same total kinetic energy Ktot as they move.
(a) Derive expressions for the translational speed of the center of mass of each object in terms of Ktot, M, and any necessary constants.
(b) Determine the ratio vBvA of the translational speeds of the cylinder to the sphere.
(c) Explain physically why the object with the larger translational speed can still have the same total kinetic energy as the other object.
(d) If both objects enter an incline high enough to bring them momentarily to rest at the same vertical height, explain whether the ratio found in part (b) will remain the same, increase, or decrease while they climb the incline. Support your answer with reasoning that references energy transformations.