A solid cylindrical merry-go-round of radius and rotational inertia about its central…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A solid cylindrical merry-go-round of radius R and rotational inertia I about its central vertical axis rotates freely with an initial angular speed ω0. Four identical children, each of mass m, stand at the very rim and rotate together with the platform.
At one instant, two of the children walk radially inward and stop at a distance R/2 from the axis, while the other two remain at the rim. During the brief interval in which the children move, any frictional torque on the system is negligible.
Answer the following questions about the situation once all motion of the children relative to the platform has ceased.
(a) Rank, from greatest to least, the following quantities for the system *after* the children have moved compared with their values *before* the children moved. Use the symbols ">", "<", or "=", and justify any ties.
i. Magnitude of the total angular momentum about the central axis
ii. Total rotational kinetic energy
iii. Angular speed of the merry-go-round
(b) Provide a qualitative explanation for each ranking above. In your discussion, identify the physical principle that constrains the angular momentum of the system and explain why the rotational kinetic energy changes even though the external torque is negligible.