Question 8.17: THE SPINNING STOOL GOAL Apply conservation of angular moment...
THE SPINNING STOOL
GOAL Apply conservation of angular momentum to a simple system.
PROBLEM A student sits on a pivoted stool while holding a pair of weights. (See Fig. 8.36.) The stool is free to rotate about a vertical axis with negligible friction. The moment of inertia of student, weights, and stool is 2.25 \mathrm{~kg} \cdot \mathrm{m}^{2}. The student is set in rotation with arms outstretched, making one complete turn every 1.26 \mathrm{~s}, arms outstretched. (a) What is the initial angular speed of the system? (b) As he rotates, he pulls the weights inward so that the new moment of inertia of the system (student, objects, and stool) becomes 1.80 \mathrm{~kg} \cdot \mathrm{m}^{2}. What is the new angular speed of the system? (c) Find the work done by the student on the system while pulling in the weights. (Ignore energy lost through dissipation in his muscles.)
STRATEGY (a) The angular speed can be obtained from the frequency, which is the inverse of the period. (b) There are no external torques acting on the system, so the new angular speed can be found with the principle of conservation of angular momentum. (c) The work done on the system during this process is the same as the system’s change in rotational kinetic energy.
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