Turntable Rotation with weight on edge v. in the center

[AROD]

Homework Statement

A man (mass m1 = 100 kg) stands at the fringe of the large rotary table (radius R = 5 m, massm2 = 100 x m1), which rotates at a frequency of 10/min. The man goes along a radius line towards the table center until he reaches the rotation axis. The spatial extent of the man should be neglected.
a) How does the rpm (revolutions per minute) number of the rotary table change (in absolute
und relative terms)?
b) The man has to work against the centrifugal force in order to get to the center of the table.
Show that the work done by the man amounts to the increase of the rotational energy of theentire system.

Homework Equations

conservation of momentum: p = p1 + p2
rotational energy : 1/2mr^2w^2

The Attempt at a Solution

Period of 36s with man on edge. How is it different when he is in the middle?

 

[LowlyPion]

Your angular momentum can be expressed as I*ω

So won't your I*ω before = I*ω after?

Figure then your I with the 1kg at the edge and 1 kg at the center.

I before = 1/2m*(5)² + 1*5²

What is it after his walk? Then you can figure what happens to ω can't you?

 

[Delphi51]

How is it different when he is in the middle?

It's not if a motor is maintaining the 10 RPM.
On the other hand, if we have no motor, the thing will speed up as the man's mass moves toward the center like a skater spins faster when his arms are held closer. Maybe you are supposed to use conservation of angular momentum to figure this out.

 

[AROD]

moment of inertia for this disk is 1/2*(mass disk)*r^2 and before with the man on the edge the total inertia is plus also 1/2*(mass man)*(position)^2 ?

and at the end the man is in the center so his distance from center of mass is 0 and doesn't contribute to the intertia, just the total mass

 

[Delphi51]

That looks great, Arod. I think Lowly Pion typoed the mass of the man in his message.

 

[LowlyPion]

That looks great, Arod. I think Lowly Pion typoed the mass of the man in his message.

Sort of. I calculated it as the turntable being 100 and the man as 1 according to the 100:1 and dropped out m1. My typo really was in not relating that step.