A 55.0-kg woman stands at the rim of a horizontal turntable having a moment of i

Question

A 55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 480 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 clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth.

(a) In what direction does the turntable rotate?

clockwisecounterclockwise    

With what angular speed does the turntable rotate?
rad/s

(b) How much work does the woman do to set herself and the turntable into motion?
J

Explanation / Answer

A. as the woman starts walking the turntable must develop a counter-clockwise momentum whose magnitude should be equal to woman's clockwise angular momentum.

Counterclockwise

using angular momentum conservation

Li = Lf

Ii*wi = If*wf

mr^2*(V/r) = If*wf

wf = mVr/If

wf = 55*1.50*2/480

wf = - 0.344 rad/sec (negative sign is for counter-clockwise direction)

B. using Work-energy theoram:

W = dKE

W = 0.5mv^2 + 0.5*I*wf^2

W = 0.5*55*1.5^2 + 0.5*480*0.344^2

W = 90.28 J

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