   Chapter 8, Problem 70P

Chapter
Section
Textbook Problem

A student sits on a rotating stool holding two 3.0-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 · m and is assumed to be constant. The student then pulls in the objects horizontally to 0.30 m from the rotation axis, (a) Find the new angular speed of the student, (b) Find the kinetic energy of the student before and after the objects are pulled in.

(a)

To determine
The new angular speed of the student.

Explanation

Given info: mass of the object is 3.0kg , the moment of inertia of student plus stool system is 3.0kgm2 , distance of each object from the axis of rotation is 1.0m and the initial angular speed of the system is 0.75rad/s .

Explanation: The initial moment of inertia of the system is Ii=Imasses+Istudent+stool that is Ii=2mr2+Istudent+stool . Conservation of angular momentum is used to find the angular speed.

The formula for initial moment of inertia of the system is,

Ii=2mr2+Istudent+stool

• m is mass of the object.
• r is distance of each object from the axis of rotation.
• Istudent+stool is moment of inertia of student plus stool system.

Substitute 3.0kg for m , 1.0m for r , and 3.0kgm2 for Istudent+stool to find Ii .

Ii=2(3.0kg)(1.0m)2+3.0kgm2=9.0kgm2

Thus, the initial moment of inertia of the system is 9.0kgm2 .

The formula for final moment of inertia of the system is,

If=2mr2+Istudent+stool

• m is mass of the object.
• r is distance of each object from the axis of rotation.
• Istudent+stool is moment of inertia of student plus stool system.

Substitute 3

(b)

To determine
The kinetic energies of the student before and after the objects are pulled in.

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