Answer to Question #272791 in Mechanics | Relativity for Hemali

Question

A star having rotational inertia of



48 2 10 10 kgm

is rotating at an angular speed

of 2.0 revolutions per month about its axis. The only force on it is the force of

gravitation. When its nuclear fuel is exhausted, it shrinks to a neutron star

having rotational inertia of



48 2 6.0 10 kgm .

Determine the angular speed

of the neutron star in revolutions per month.

Answer 1

The angular momentum of the star is conserved:

$$L_i=L_f,\\\space\\ I_i\omega_i=I_f\omega_f,\\\space\\ \omega_f=\omega_i\frac{I_i}{I_f},\\\space\\ \omega_f=2·\frac{10·10^{48}}{6·10^{48}}=3.3\text{ rev/month}$$