A student sitting on a frictionless rotating stool has rotational inertia 0.91 k

Question

A student sitting on a frictionless rotating stool has rotational inertia 0.91kg?m2 about a vertical axis through her center of mass when her arms are tight to her chest. The stool rotates at 7.25rad/s and has negligible mass. The student extends her arms until her hands, each holding a 4.7kg mass, are 0.73m from the rotation axis.

a.) Ignoring her arm mass, what's her new rotational velocity?

b.) Repeat if each arm is modeled as a 0.73m long uniform rod of mass of 4.8kg and her total body mass is 59kg .

Explanation / Answer

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conservation of angular momentum.

I1 w1 = I2 w2

I1 = 0.91   w1 = 7.25   

I2 = 0.91 + (2 * 4.7 *0.73^2) = 6.48

w2 = 0.91 * 7.25 / 6.48

= 1.1 rad/sec

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In the second case I2 = 0.91 + (4.7 * 2 * 0.365^2) = 2.16

w2 = 0.91 * 7.25 / 2.16

w2 = 3.05 rad/sec

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