Question

A star may collapse into an extremely dense body (called neutron star ) composed predominantly of neutrons. This can happen when massive stars die in supernovas and their cores collapse. Represent the star as a uniform solid sphere both before and after the collpase. Assume no astronomical bodies are in the vicinity of the star, so no forces or torques are exerted on the star. The star’s initial radius was 9.45 × 108 m, its final radius is 15200 m, mass remains the same and the original star made 1 revolution every 20 days. Calculate the angular speed of the neutron star.

Answer 1

There are no external Torques, so angular momentum is conserved

initial angular velocity x I1 = I2 x final angular velocity

final angular velocity = initial angular velocity x I1/ I2

initial time period = 20 days = 20 x 24 x 60 x60 secs

initial angular velocity = 2 pi / ( 20 x 24 x 60 x 60 ) s

I1 = (2/5) x m x r^2 = 0.4 x m x (9.45 x 10^8m)^2

I2 = 0.4 x m x ( 15200m)^2

final angular velocity =.    [2 pi / ( 20 x 24 x 60 x 60 ) s] x  [0.4 x m x (9.45 x 10^8m)^2 / 0.4 x m x 15200^2 m^2

= 1.40 Radians/s