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.
The total initial angular momentum is −L (down), due
solely to the spinning wheel. To shown below. invert the wheel the student
−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
momentum is +L (up). Therefore, the change in the
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
angular momentum is −2L ! 2 ...
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