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)`. What is the angular speed of the star when it collapses (due to inward gravitational) force) to a radius of `10^(4)km`?

Explanation

During collapose, the total angular momentum of an isolated star is conserved, hence
`I_(1)omega_(1)=I_(2)omega_(2)`
or `2/5MR_(1)^(2)omega_(1)=2/5MR_(2)^(2)omega_(2)[ :'I=2/5MR^(2)]`
or `R_(1)^(2)omega_(1)=R_(2)^(2)omega_(2):. Omega_(2)=(R_(1)^(2))/(R_(2)^(2))omega_(1)`
But `R_(1)=10^(6)km, R_(2)=10^(4)km, omega_(1)=10^(-6)s^(-1)`
`:.` Angular speed`omega_(2)=((10^(6))^(2))/((10^(4))^(2))xx10^(-6)=10^(-2)`
`=0.01"rad"s^(-1)`