|Nov13-10, 07:56 PM||#1|
2 people 1 rotating disc
1. The problem statement, all variables and given/known data
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
3. 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.
|Nov14-10, 07:16 AM||#2|
there is a torque, because there is a tangential acceleration …
the students not only have a centripetal acceleration they also are changing their tangential component of velocity, and so have a tangential acceleration, which must be provided by a tangential force
(in a frame of reference rotating with the plate, that would be a Coriolis force , 2mω x vrel, perpendicular to the relative velocity, which is radial)
… that tangential force provides a torque on the students, increasing their angular momentum (and the students provide an opposite torque on the plate, decreasing its angular momentum, so there's no overall torque and no overall change in angular momentum)
|Nov14-10, 03:36 PM||#3|
So the students do exert a torque, and the reason momentum is still conserved is because the plate exerts an equal and opposite torque on the students.
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