Question

A 50 kg woman stands at the rim of a horizontal turntable having a moment of...

A 50 kg woman stands at the rim of a horizontal turntable having a moment of inertia of 560 kg·m2 and a radius of 2.0 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 1.5 m/s relative to the Earth.

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

clockwise or counterclockwise

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

(a) We know that, Linitial = Lfinal

(L1 + L2)i = (L1 + L2)f

since, initially the system is at rest.

0 = (L1 + L2)f

0 = I11 + I22

1 = - I22 / I1    { eq.1 }

1 = - (m r2) (v/r) / I1

1 = - m r v / I1 = - [(50 kg) (2 m) (1.5 m/s)] / (560 kg.m2)

{ it's direction will be counter clockwise }

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

we know that, W = K.E

W = (K.Efinal - K.Einitial)

W = [(1/2) I112 + (1/2) m v2] - (0 J)

W = [(0.5) (560 kg.m2) (-0.267 rad/s)2 + (0.5) (50 kg) (-1.5 m/s)2]

W = 76.2 J