A student sitting on a frictionless rotating stool has rotational inertia 0.88kg

Question

A student sitting on a frictionless rotating stool has rotational inertia 0.88kg* m^2 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 5.5kg mass, are 0.73m from the rotation axis. Ignoring her arm mass, what's her new rotational velocity? Repeat if each arm is modeled as a 0.73m long uniform rod of mass of 4.6kg and her total body mass is 57kg .

Explanation / Answer

A student sitting on a frictionless rotating stool has rotational inertia 0.97 kg*m2 about a vertical axis through her center of mass when her arms are tight to her chest. The stool rotates at 6.65rad/s and has negligible mass. The student extends her arms until her hands, each holding a 3.6kg mass, are 0.78m from the rotation axis. Ignoring her arm mass, what's her new rotational velocity? Repeat if each arm is modeled as a 0.78 long uniform rod of mass of 4.6 and her total body mass is 65 .

conservation of angular momentum as no torque is apllied initial

angular momentum=Iw=(0.97*6.65)=6.45 kgm2s-1

now new inertia is (0.97+2*3.6*0.78*0.78)=5.35

new angular velocity=6.45/5.35=1.20 rad/s

if her arms are also contributing in inertia

new inertia=5.35+2ml^/3==7.22

angular velocity=6.45/7.22=0.89rad/s

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