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brushman
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Homework Statement
A large plate is balanced at its center and two students of equal mass stand at its center. The plate is
rotated on a frictionless pivot about an axis through its center and perpendicular to its face. The students
then begin to walk out towards opposite edges.
(Select T-True, F-False, I-Increases, D-Decreases, S-Stays the same. ).
A) The students do no work in walking outward. False: The students do work against the centripetal force
B) The students produce a net torque on the plate. True: The rate of rotation slows down, there has to be a
torque to do that.
C) The rate of rotation ... as the students walk outward. Decreases: angular momentum is conserved,
moment of inertia increases so angular velocity has to decrease
D) The total angular momentum of the system ... as the students walk outward. :Same: closed system,
angular momentum is conserved
E) When the students reach the outer edge and stop, the moment of inertia of the system (plate+students)
is the same as when the students started. F: it increases
The Attempt at a Solution
As you can see, the correct answers are already there. What I don't under stand is B and C. Isn't this a direct contradiction? If there's a torque, then momentum must not be conserved, right?
What's the explanation for this!? I guess because it's a closed system. But wouldn't that also mean that kinetic energy is conserved which isn't necessarily true since omega is squared in the rotational energy, 1/2 Iw^2.
For example, if the kids started at the edge and walked in the kinetic energy would increase right?
I also don't see how the students would produce a net torque. It seems like their torques would cancel each other out.
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