Question

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    

rad/s

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

Answer 1

(a) We know that, L_initial = L_final

(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)

₁ = 0.267 rad/s

{ 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.E_final - K.E_initial)

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