a man is sitting on a spinning chair, the moment of enertia for the man ane chair si 5kgm(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}, 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}=5kgm^{2}=const

I_{massi}=MR_{i}^{2}=12kgm^{2}

I_{massf}=MR_{f}^{2}0.48kgm^{2}

[tex]\omega[/tex]_{i}=0.5[tex]\pi[/tex]rad/s

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

I_{i}[tex]\omega[/tex]_{i}=I_{f}[tex]\omega[/tex]_{f}

(5+12)*0.5[tex]\pi[/tex]=(5+0.48)[tex]\omega[/tex]_{f}

[tex]\omega[/tex]_{f}=[tex]\frac{(5+12)*0.5[tex]\pi[/tex]}{(5+0.48)}[/tex]=4.873rad/s

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what is the work done by the man?

W=[tex]\Delta[/tex]E

all the changes are in kinetic energy so

W=Ek_{f}-Ek_{i}=(0.5I[tex]\omega[/tex]^{2})_{f}-(0.5I[tex]\omega[/tex]^{2})_{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??

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# Homework Help: Am i going about this correctly? momentum

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