The mass of a star is 1.61·1031 kg and its angular velocity is 1.40E-7 rad/s. Find its new angular velocity if the diameter suddenly shrinks to 0.17 times its present size.

Question

Assume a uniform mass distribution before and after. Icm for a solid sphere of uniform density is 2/5 mr2.

Answer 1

I₁ω₁ = I₂ω₂; 2/5mR₁²ω₁ = 2/5mR₂²ω₂; ω₂ = ω₁R₁²/R₂² = 1.4·10^-7/0.17² = 4.8443·10^-6 rad/s