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

AI Thread Summary
Changing arm position affects angular velocity and work done due to the conservation of angular momentum. When the man lowers his arms, his moment of inertia decreases, resulting in an increase in angular velocity, calculated as omega_1 = 2 omega_0. The work done, U, to change his body configuration is derived from the difference in kinetic energy before and after the change, expressed as U = 0.5*I_0*(omega_0)^2 - 2mgl. The calculations for angular velocity are understood, but the approach to calculating work done requires clarity on energy principles. Understanding these relationships is crucial for solving similar physics problems effectively.
PeterPoPS
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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


 
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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
 

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