A 59.0 kg woman stands at the rim of a horizontal turntable having a moment of i

Question

A 59.0 kg woman stands at the rim of a horizontal turntable having a moment of inertia of 535 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 counterclockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth.

(a) In what direction and with what angular speed does the turntable rotate? rad/s

clockwise or counterclockwise

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

Explanation / Answer

a) initial system was at rest. so initial angular momentum is zero.

using angular momentum conservation,

0   = mvR + Iw

0 = ( 59 x 1.50 x 2 ) + ( 535 w)

w = - 0.331 rad/s

angular speed = 0.331 rad/s

direction = clockwise

b) Using work energy theorem,

work done = change in KE

W = ( mv^2 /2 + Iw^2 /2) - 0

W = ( 59 x 1.50^2 /2) + ( 535 x 0.331^2 / 2)   = 95.65 J

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