Physics - Rotation

Question

Two ice skaters are holding opposite sides of a large, very flexible spring. When they are 1 m apart they are turning in a circle at about 2 Hz (cycles/s). If, while turning, they stretched their spring to 2 m in length, at what rate would they be turning in a circle?

Answer 1

Apply conservation of angular momentum, I₀ω₀ = Iω; since 2 point masses - I = 2mr²

I₀ = 2m(.5²) = .5m; I = 2m(1²); ω₀ = 2 rev/1s x (2∏ rads)/1rev = 4∏ rads/s

applying formula for conservation of angular momentum: ω = I_oω_{o / I} = .5m(4∏)/2m = ∏ rads/s

rate in term of revolutions ∏rad/s x 1 rev./2∏ rad = .5 rev/s = .5 Hz