A student is seated on a low-friction swivel stool that can rotate freely about a…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A student is seated on a low-friction swivel stool that can rotate freely about a vertical axle through the stool’s center. A friend standing 2.0m directly in front of the student (measured horizontally) throws a 0.25kg rubber ball horizontally toward the student, who catches it at chest height. The ball’s velocity just before the catch is 5.0ms−1 directed straight toward the student. Neglect air resistance and assume the catching interval is very short compared with any other times in the problem.
Throughout your answers, treat the Earth, the stool, and the student as external to the ball–student system unless explicitly included.
(a) State whether total angular momentum for the ball–student system can be taken as conserved about a vertical axis through the student’s center of mass during the catching process. Justify your answer by discussing any external torques about that axis.
(b) Consider instead a vertical axis that passes through the friend (the point from which the ball is thrown). Is the total angular momentum of the ball–student system conserved about this axis during the catch? Explain your reasoning in terms of external forces and their lines of action.
(c) Compare the two axes considered in parts (a) and (b). Describe how choosing one axis over the other would affect the mathematical form of an equation expressing angular momentum conservation, and explain why one choice is preferable for quantitative analysis of the student’s subsequent rotation.