Am i going about this correctly? momentum

[Dell]

a man is sitting on a spinning chair, the moment of enertia for the man ane chair si 5kgm², the man has in each hand a mass of 6kg, held at 1m from the centre of the chair, parallel to the ground. the man completes one rotation every 4 seconds. now he moves the messes close to his body(0.2m from the centre of rotation)

what is the new rotational velocity?

I_mani=5kgm²=const
I_massi=MR_i²=12kgm²
I_massf=MR_f²0.48kgm²
\omega_i=0.5\pirad/s

now i know that the angular momentum is conserved since there is no external torque, so

I_i\omega_i=I_f\omega_f
(5+12)*0.5\pi=(5+0.48)\omega_f

\omega_f=\frac{(5+12)*0.5\pi}{(5+0.48)}=4.873rad/s
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what is the work done by the man?

W=\DeltaE
all the changes are in kinetic energy so

W=Ek_f-Ek_i=(0.5I\omega²)_f-(0.5I\omega²)_f
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what is the actual force that causes the increase in velocity?? i understand the principle- that the smaller the radius the smaller the moment of enertia ans therefore the larger the velocity in order to conserve the momentum, but what physically makes him move faster??

 

[Doc Al]

what is the actual force that causes the increase in velocity??

The man provides that force. It takes work to pull those masses closer to the axis. His arms must exert a force to pull them in.