A student sits on a rotating stool holding two 2.8-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 2.8-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg · m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.50 m from the rotation axis.

(a) Find the new angular speed of the student.
rad/s

(b) Find the kinetic energy of the student before and after the objects are pulled in.

Explanation / Answer

Here ,

initial moment of inertia of student , I1 = 3 + 2 * 2.8 * 1^2

I1 = 8.6 Kg.m^2

final moment of inertia , I2 = 3 + 2 * 2.8 * 0.5^2

I2 = 4.4 Kg.m^2

a)

new angular speed of the student is wf

wf * I2 = I1 * wi

4.4 * wf = 8.6 * 0.75

wf = 1.47 rad/s

the new angular speed of the student is 1.47 rad/s

b)

kinetic energy before = 0.5 * I * wi^2

kinetic energy before = 0.5 * 3 * 0.75^2

kinetic energy before = 0.844 J

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kinetic energy after = 0.5 * I * wf^2

kinetic energy after = 0.5 * 3 * 1.47^2

kinetic energy after = 3.24 J

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