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A professor sits on a rotating stool that spins at 10.0rpm while she holds a 1.00-kg...

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Physics

A professor sits on a rotating stool that spins at 10.0rpm whileshe holds a 1.00-kg weight in each of her hands. Her outstretchedarms are 0.75m from the axis of rotation which passes through herhead into the center of the stool. When she draws the weights intoward her body, her angular speed increases to 20.0 rpm.Neglecting the mass of her arms, how far are the weights from therotational axis at the increased speed?

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4.0 Ratings (747 Votes)

here conservation of angular momentum

that is

Li = Lf       initial angular momentum = final angular momentum

we know that angular momentum L = Iw    I is sum of moment of inertia of two weights of mass 1 kr each

Li = (mr1^2 +mr1^2)wi= 2mr1^2*wi

Lf = (mr2^2 +mr2^2)wf= 2mr2^2*wf

Li = Lf === > 2mr1^2*wi = 2mr2^2*wf

                 r2= r1(sqrt (wi / wf))

                      = 0.75 sqrt(10*2*pi / 20*2*pi)

                      = 0.75 sqrt(1/2)

                   r2 = 0.53033 m

the new position of the weights from the rotational axis is 0.53033 m
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