Question 16 of 17 Map University Physics Kesten Tauck presented by Sapling Learn

Question

Question 16 of 17 Map University Physics Kesten Tauck presented by Sapling Learning A professor sits on a rotating stool that is spinning at 10.0 rpm while she holds a heavy weight in each of her hands. Her outstretched hands are 0.765 m from the axis of rotation, which passes through her head into the center of the stool. When she symmetrically pulls the weights in closer to her body, her angular speed increases to 28.5 rpm. Neglecting the mass of the professor, how far are the weights from the rotational axis after she pulls her arms in? Number

Explanation / Answer

Given

Initial angular velocity = 10.0 rpm

Location of weights from the axis of rotation s = 0.765 m

Final angular velocity ’ = 28.5 rpm

Solution

= 10.0 rpm

= 10.0 x 0.1047 rad/s

= 1.047 rad/s

’ = 28.5 rpm

’ = 28.5 x 0.1047

’ = 2.983 rad/s

The initial moment of inertia of the system of weights.

I = 2 x (Mass x s2)

I = 2 x (M x 0.7652)

I = 1.17045M

The initial angular momentum

L = I

L = 1.17045M x 1.047

L = 1.23M

The final angular momentum = Initial angular momentum

L’ = L

I’’ = I

I’ = I/’

2(Ms’2) = 2(Ms2)/’

s’2 = s2/’

s’2 = 0.7652(1.047/2.983)

s’ = 0.453 m

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