A student sitting on a frictionless rotating stool has rotational inertia 0.95 k

Question

A student sitting on a frictionless rotating stool has rotational inertia 0.95 kg m2 about a vertical axis through her center of mass when her arms are tight to her chest. The stool rotates at 6.80 rad/s and has negligible mass. The student extends her arm until her hands, each holding a 5.0 kg mass, are 0.75 m from the rotation axis. (a) Ignoring her arm mass, what's her new rotational velocity? (b) Repeat if each arm is modeled as a 0.75 m long uniform rod of mass of 5.0 kg and her total body mass is 65 kg.

Explanation / Answer

here,

initial rotational inertia , Ii = 0.95 kg.m^2

initial angular velocity , wi = 6.8 rad/s

(a)

the moment of inertia , If = Ii + 2* 5 * 0.75^2

If = 6.575 kg . m^2

let the new angular velocity be wf

using conservation of angular momentum

If * wf = Ii * wi

6.575 * wf = 0.95 * 6.8

wf = 0.98 rad/s

(b)

the moment of inertia , If = Ii + 2 * ( 1/3) * 5 * 0.75^2

If = 2.825 kg . m^2

let the new angular velocity be wf

using conservation of angular momentum

If * wf = Ii * wi

2.825 * wf = 0.95 * 6.8

wf = 2.29 rad/s

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