Circular disk rotates with student on it

[bearhug]

A horizontal platform in the shape of a uniform circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a mass of 150 kg, and radius of 2.00 m. A 60kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.5 rad/s when the student starts walking, what is the angular speed when she is 0.50 m from the center?

I originally used the equation Li=Lf
where Li= Iw= (1/2)(MR^2)wi which equals (.5)(210kg)(2.0^2)(1.5rad/s)
Li= 630
Lf= (If1+ If2)(wf)
=[(.5)(150)(2.0^2) + (60)(0.5^2)]wf
This gave me wf= 2.0 rad/s but that doesn't seem to make sense wouldn't the angular speed slow down as the student went closer to the center? Any hints as to where I went wrong is greatly appreciated.

 

[BishopUser]

Angular velocity wouldn't necessarily slow down as you go towards the center. Ever watch figure skating where a skater starts a spin with his legs/arms extended and as he brings his arms/legs closer he begins to spin much quicker? Ever watch divers do multiple flips, they bring as much mass as possible close to their axis of rotation to spin fast then when they want to stop they extend their arms and legs to finish the dive.

 

[Doc Al]

I originally used the equation Li=Lf
where Li= Iw= (1/2)(MR^2)wi which equals (.5)(210kg)(2.0^2)(1.5rad/s)

You have computed the wrong initial value for I of the system, which will give you a wrong value for Li.

Li= 630
Lf= (If1+ If2)(wf)
=[(.5)(150)(2.0^2) + (60)(0.5^2)]wf

This time you computed the final rotational inertia properly. (Fix your initial value accordingly.)

This gave me wf= 2.0 rad/s but that doesn't seem to make sense wouldn't the angular speed slow down as the student went closer to the center?

What happens to the rotational inertia of the system as the person moves closer to the center? (Does it increase or decrease?) Then consider that L = Iiwi = Ifwf.

 

[bearhug]

Thanks for the advice. Since only the initial value is incorrect I am under the impression that it is the Mass that is wrong. Originally I included both the student and the platform in the mass because I interpreted the problem as the student already being on the platform at the beginning. However that doesn't seem to be giving me the correct initial. So is that because the student isn't actually on the platform in the beginning? Thanks

 

[Doc Al]

The student is on the platform from the beginning. For some reason, when calculating the intial rotational inertia of the system you just added the masses instead of adding the rotational inertias of disk and student.