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 middot m2 about a vertical axis through her center of mass when her arms are tight to her chest. The stool rotates at 7.00rad/s and has negligible mass. The student extends her arms until her hands, each holding a 5.0kg mass, are 0.80m from the rotation axis. Ignoring her arm mass, what's her new rotational velocity? Express your answer to two significant figures and include the appropriate units. Repeat if each arm is modeled as a 0.80m long uniform rod of mass of 4.9kg and her total body mass is 57kg. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

(a)

I(i) = 0.96 kg.m^2

I(f) = 0.96+2*5*0.8^2 = 7.36 kg-m^2

I(i)*w(i)=I(f)*w(f)

0.96*7 = 7.36*w(f)

w(f) = 0.913 rad/s

(b)

w' = (0.96*7)/[0.0.96*(47.2/57)+{(9.8*1.6^2)}

=0.2596 rad/s

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