discussion_problems10 - DISCUSSION PROBLEM[10.1 answers...

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Unformatted text preview: DISCUSSION PROBLEM [10.1]: ... answers ... DISCUSSION PROBLEM [10.1]: A rotating cloud of gas begins to collapse under • The moment of inertia is I = ∑i mi ri2. As ri decreases, so does the moment of inertia. gravitational forces within. As it collapses, what happens to its: • Provided there are no collisions with other gas clouds or galaxies, there are no external torques acting • Moment of inertia? on the cloud and so angular momentum is constant. • Angular momentum? • Angular velocity? • If angular momentum is conserved, then the angular velocity must increase (I1ω1 = I2ω 2) if the moment of inertia decreases. 1 DISCUSSION PROBLEM [10.2]: A student sits on a stool that is free to rotate. She is handed a wheel that is spinning in the horizontal plane as DISCUSSION PROBLEM [10.2]: answer ... Take the student, the stool and the wheel as the system. r The total initial angular momentum is −L (down), due solely to the spinning wheel. To shown below. invert the wheel the student r −L applies a torque, which is internal to the system. Since there are no external torques, angular momentum is conserved. After Assuming she (and the stool) are stationary to begin with, what happens if she inverts the wheel (through 180o) ? the wheel is inverted its angular r momentum is +L (up). Therefore, the change in the r r r angular momentum of the wheel is L − ( −L) = 2L . So how is the total angular momentum conserved? ... by having the student (and stool) rotate so their combined r angular momentum is −2L ! 2 ...
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