A star of mass equal to two solar masses and radius `10^(6) km` rotates about its axis with an angular speed of `10^(-6)rad s^(-1)`. What is the angular speed of the star, when it collapses (due to inward gravitational forces) to a radius of `10^(4) km`?

Explanation

Here, `R_(1) = 10^(6) km`,
`omega_(1) = 10^(-6) rad s^(-1), omega_(2) = ? R_(2) = 10^(4) km`
As `I_(1) omega_(1) = I_(2)omega_(2)`
`:. omega = (I_(1) omega_(1))/(I_(2)) = ((2)/(5)MR_(1)^(2) omega_(1))/((2)/(5)MR_(2)^(2)) = ((R_(1))/(R_(2)))^(2) omega_(1)`
`omega_(2) = ((10^(6))/(10^(4))) xx 10^(-6) = 10^(-2) rad//s`