A person stands, hands at their side, on a platform that is rotating at a rate of 1.50 rev/sec. When they raise their hands to a horizontal position, the rate of rotation decreases to 0.70 rev/sec. By what factor has their moment of inertia changed going from hands at side to hands outstretched? a. 2.14
b. 1.05
c. 0.467
d. None

The value is k =  2. 14

Explanation:

From the question we are told that

    The angular speed of the platform when the hands are on the side is

     The angular speed of the platform when the hands are in horizontal position is

Generally the angular momentum of the system (the person and the platform) when the person's hand is at the side is

Generally the angular momentum of the system (the person and the platform) when the person's is stretched out horizontally  is

Generally from the law of angular momentum conservation we have that

=>      

=>    

=>    

=>    

So the factor by which  moment of inertia changed is  k =  2. 14

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