How Does Changing Arm Position Affect Angular Velocity and Work Done?

[PeterPoPS]

Homework Statement

A man is standing on a rotating plate (rotates without friction). In case A he is hold 1weight in each hand (straight out) with the mass m and he is rotatin with angular velocity omega_0.
Then he moves his arms down so they are parallell to the body (case B) and increases his angular velocity to omega_1.
Calculate the new angular velocity omega_1 and the work U which the man must do to change his body configuration to case B.
You can assume that the moment of inertia on z-axis for the man is I_0 in case A and I_0 / 2 in case B.
The length of the arms of the man is l, so each weight are l units out in case A and lowered l units (and ofcourse moved l units toward the body) in case B.

the answers are given
omega_1 = 2 omega_0
and
U = 0.5*I_0*(omega_0)^2 - 2mgl


My Problem is i get how to calculate the angular velocity omega_1
But I don't understand how to even start on calculating the work done.

Best regards /Peter

Homework Equations

The Attempt at a Solution

 

[member 553083]

For omega_1 I used the formulaI = I_0 + 2ml^2so I_1 / I_0 = omega_1 / omega_0and then got that omega_1 = 2 omega_0