A student (treated as a uniform cylinder of mass 60 kg and radius 0.20 m) stands at…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A student (treated as a uniform cylinder of mass 60 kg and radius 0.20 m) stands at rest on the friction-less, horizontal surface of a lightweight circular turntable that can rotate about a vertical axle through its center. The turntable itself has mass 15 kg and radius 0.75 m. Initially, the student is holding a 3.0-kg medicine ball in each outstretched hand; the balls are 0.75 m from the axle. With feet firmly planted, the student and turntable together are set spinning at 1.0 rad/s.
After the rotation has reached this constant rate, the student carefully draws both medicine balls straight inward until they are 0.30 m from the axle. Immediately afterward, without changing body position, the student releases one of the balls so that it lands and sticks to the rim of the turntable (0.75 m from the axle) without rebounding. Treat all objects as moving only in the horizontal plane.
(a) Calculate the total angular momentum of the system (student + turntable + both balls) about the axle just before the student begins to move the balls inward.
(b) Determine the new angular speed of the student and turntable after both balls have been pulled inward but before either ball is released.
(c) Find the final angular speed of the combined system (student + turntable + 2 balls) after one ball has stuck to the rim and the other ball remains held at 0.30 m from the axle.
(d) Explain how conservation principles justify the calculations in parts (b) and (c), explicitly identifying the system you considered and discussing any external torques.