   Chapter 8, Problem 68P

Chapter
Section
Textbook Problem

A 60.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 500 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clock-wise (as viewed from above the system) at a constant speed of 1.50 m/s relative to Earth. (a) In what direction and with what angular speed does the turntable rotate? (b) How much work does the woman do to set herself and the turntable into motion?

(a)

To determine
The angular speed and the direction of a turntable.

Explanation

Given info: The moment of inertia of the table is 500kgm2 , mass of the woman is 60.0kg for mw , the radius of the turn table is 2.00m , and the initial angular speed of the woman is 1.50m/s .

Explanation: The initial angular momentum of the turntable is equal to the final angular momenta of turn table and the woman. Assume that the angular momentum is positive if directed upward and negative if it is directed downward. So, the conservation of angular momentum of the system is Li=Lf0=Itωt+Iwωw hence they start from rest and the moment of inertia of the woman is Iw=mr2 . By rearranging this expression, the final angular speed of the table is calculated.

The formula for the final angular speed of the turntable is,

ωt=(mwrIt)vw

• It is moment of inertia of the turntable.
• mw is mass of the woman.
• r is radius of the turntable.
• vw is translational velocity of the woman

(b)

To determine
The work done by the women do to set herself and the turn table into motion.

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