A professor sits on a rotating stool that spins at 10.0 rpm while she holds a 1.

Question

A professor sits on a rotating stool that spins at 10.0 rpm while she holds a 1.00-kg weight in each of her hands. Her out- stretched  arms  are  0.750  m  from  the  axis  of  rotation,  which passes  through  her  head  into  the  center  of  the  stool.  When she  draws  the  weights  in  toward  her  body,  her  angular  speed increases to 20.0 rpm. Neglecting the mass of her arms, how far are the weights from the rotational axis at the increased speed? A professor sits on a rotating stool that spins at 10.0 rpm while she holds a 1.00-kg weight in each of her hands. Her out- stretched  arms  are  0.750  m  from  the  axis  of  rotation,  which passes  through  her  head  into  the  center  of  the  stool.  When she  draws  the  weights  in  toward  her  body,  her  angular  speed increases to 20.0 rpm. Neglecting the mass of her arms, how far are the weights from the rotational axis at the increased speed?

Explanation / Answer

moment of inertia in the initial case I1=2*(1*0.75^2)=1.125

initial rpm=w1=10

final rpm=w2=20

final moment of inertia=I2

now angular momentum has to be the same,

I1*w1=I2*w2

so

1.125*10=I2*20

I2=0.5625=2*1*r^2

r=0.53m

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