A55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 540 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? counterclockwise or clockwise
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

a) ω = 0.305 rad/s counterclockwise

b) W = 61.875J

Explanation:

The angular speed of the woman is:

By conservation of the angular momentum:

 where ωo = 0

Solving for :

Work done by the woman is given by the variation on her kinetic energy:

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

measuring things 1 litre of water