A student sitting on a frictionless rotating stool has rotational inertia 0.96kg

Question

A student sitting on a frictionless rotating stool has rotational inertia 0.96kg*m2 about a vertical axis through her center of mass when her arms are tight to her chest. The stool rotates at 6.95rad/s and has negligible mass. The student extends her arms until her hands, each holding a 5.3kg mass, are 0.76m from the rotation axis.

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

Repeat if each arm is modeled as a 0.76m long uniform rod of mass of 5.0kg and her total body mass is 59kg .

Explanation / Answer

a)

new rotaional inertia = 0.96+ 2*5.3*0.762 = 7.1 kg-m2

new rotational velocity = 0.96*6.95/7.1 = 0.94 rad /s

b)

new rotaional inertia = (0.96*49/59) + 2*5.3*0.762 +2*1/3*5*0.762 = 8.85 kg-m2

new rotational velocity = 0.96*6.95/8.85 = 0.75 rad /s

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