An acrobatic physics professor stands at the center of a turntable holding his a

Question

An acrobatic physics professor stands at the center of a turntable holding his arms extended horizontally with a 5.0 kg dumbbell in each hand. He is set rotating about a vertical axis, making one revolution in 2.0 s. Find the profs new angular velocity if he pulls the dumbbell in to his stomach. His moment of inertia (without the dumbbells) is 3.0 kgm^2 when his arms out-stretched, dropping to 2.2 kg.m^2 when his hands are at his stomach. The dumbbells are 1.0 m from the axis initially and 0.20 m from it at the end. Treat the dumbbells as particles.

Explanation / Answer

number of revoluton N=1

time T=2 s

the angular velocity his arms are streached W1=2*3.14*1/2=3.14 rad/s

the momentum of inertia his hand streached =>I1=3 kg.m^2

momentum of inertia of his hand is stomach =>,I2=2.2 kg.m62

this concept is basing on law of conservation of angular momentum

so=>I1W1=I2w2

3*3.14=2.2 W2

therefore the angular velocity his hands are stomach W2=4..3 rad/s

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