Do the students exert a net torque on the rotating disc?

[brushman]

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.

 

[tiny-tim]

hi brushman!

there is a torque, because there is a tangential acceleration …

the students not only have a https://www.physicsforums.com/library.php?do=view_item&itemid=27" 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 https://www.physicsforums.com/library.php?do=view_item&itemid=86" , 2mω x v_rel, perpendicular to the relative velocity, which is radial)

… that tangential force provides a torque on the students, increasing their https://www.physicsforums.com/library.php?do=view_item&itemid=313" on the plate, decreasing its angular momentum, so there's no overall torque and no overall change in angular momentum)

 

[brushman]

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.

Thanks.