How Much Work Does a Woman Do to Start a Turntable in Motion?

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SUMMARY

The discussion focuses on calculating the work done by a 62 kg woman to initiate motion on a horizontal turntable with a moment of inertia of 540 kg·m² and a radius of 2.1 m. As she walks clockwise at a speed of 1.5 m/s, the angular speed of the turntable reaches 0.361667 rad/s. The kinetic energy of the system is calculated using the formula KErotational = (1/2)Iω², resulting in a work output of 22.1429 J. The analysis raises questions about the presence of external torque affecting the system.

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1. A 62 kg woman stands at the rim of a horizontal turntable with a moment of inertia of 540 kg·m2 and a radius of 2.1 m. The system is initially at rest, and the turntable is free to rotate about a frictionless vertical axle through its center. The woman then starts walking clockwise (when viewed from above) around the rim at a constant speed of 1.5 m/s relative to the Earth. If it helps the angular speed of the turntable is .361667 rad per second. How much work does the woman do to set the system in motion?


2. KErotational=(1/2)IW^2
Angular velocity = W = Vt/R
I=MR^2



3. KErotational=1/2(62*2.1)(1.5/2.1)^2
KErotational=22.1429
KErotational=0
Work=Change in KE
W=22.1429J
 
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Was there any external torque on the system? Does that suggest anything?
 

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