A star of mass twice the solar mass and radius 10^6 km rotates about its axis with an angular speed of 10^-6 rad/s^-1.

Question

A star of mass equal to two solar masses and radius 10⁶ km rotates about its axis with an angular speed of 10^-6 rads^-1. What is the angular speed of the star, when it collapses (due to inward gravitational forces) to a radius of 10⁴ km?

Answer 1

Here, R₁ = 10⁶ Km

ω₁ = 10^-6 rads^-1, ω₂ = ? R₂ = 10⁴ Km

As I₁ω₁ = I₂ω₂

\(\therefore\) ω = \(\frac{I_1\omega_1}{I_2}=\cfrac{\frac25MR_1^2\omega_1}{\frac25MR_2^2}\)

\(=(\frac{R_1}{R_2})^2\)ω₁

ω₂ = \(\left(\frac{10^6}{10^4}\right)\)x 10^-6 = 10^-2 rad/s