A rigid platform rotates about a vertical axis

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A rigid platform rotates about a vertical axis. Its angular momentum LL (in kg⋅m2/s\text{kg}\cdot\text{m}^2/\text{s}) varies with time tt (in s\text{s}) as follows: • 0≤t≤3 s0 \le t \le 3\,\text{s} : LL increases uniformly from −6-6 to 00. • 3≤t≤5 s3 \le t \le 5\,\text{s} : LL increases uniformly from 00 to 66. • 5≤t≤7 s5 \le t \le 7\,\text{s} : LL remains constant at 66. • 7≤t≤9 s7 \le t \le 9\,\text{s} : LL decreases uniformly from 66 to 22. Answer the questions below about the external torque acting on the platform. (a) On your own axes of torque (vertical) versus time (horizontal), sketch a qualitative graph of the net external torque acting on the platform for 0≤t≤9 s0 \le t \le 9\,\text{s}. Clearly indicate constant sections and abrupt changes. (b) Identify the single instant, if any, at which the net external torque is 00 while the angular momentum is still changing. Justify your answer. (c) Explain how the shape of your torque graph in part (a) reflects the features of the stated angular-momentum variation.

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