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

AI Thread Summary
The discussion focuses on calculating the work done by a woman to set a turntable in motion, given her mass, the turntable's moment of inertia, and her walking speed. The initial kinetic energy of the system is zero, and as she walks, the rotational kinetic energy is calculated using the formula KErotational = (1/2)Iω². The calculated work done by the woman to initiate motion is approximately 22.14 Joules. The conversation also raises the question of whether any external torque was applied to the system, hinting at implications for the dynamics involved. The analysis highlights the relationship between linear and angular motion in a frictionless environment.
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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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