A 60.0 kg woman stands at the rim of a horizontal turntablehaving a moment of in

Question

A 60.0 kg woman stands at the rim of a horizontal turntablehaving a moment of inertia of 500 kgm^2 and a radius of 2.00m. The turntable is initially at rest and is free to rotateabout a frictionless, vertical axle through its center. Thewoman then starts walking around the rim clockwise (as viewed fromabove the system) at a constant speed of 1.50 m/s relative to theEarth. a) In what direction and with what angular speed does theturntable rotate? b) How much work does the woman do to set herself and theturntable into motion?

Explanation / Answer

Angular momentum of the woman:

Li = m*v*r = 60*1.5*2 = 180 kg.m^2/s

Let the angular speed of the turntable be W

So, angular momentum of the turntable L = -180 = 500*W

So, W = -0.36 rad/s

So, It will rotate counterclockwise <------- answer (a)

b)

Work done by woman : = 0.5*m*v^2 + 0.5*I*W^2 = 0.5*1.5^2 + 0.5*500*0.36^2 = 33.53 J

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