Question

A star having rotational inertia of 10 1049 kgm2 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 6.0 x 1048 kgm². Determine the angular speed of the neutron star in revolutions per month.

Answer 1

Rotational inertia

$I_1=10\times10^{49}kgm^2$

$I_2=6\times10^{48}kgm^2$

$w_1=\frac{2\pi\times2}{30\times24\times60\times60}rad/sec$

$w_1=4.84\times\times10^{-6}rad/sec$

We know that

$I_1w_1=I_2w_2$

$w_2=\frac{I_1w_1}{I_2}$

$$w_2=\frac{10\times10^{49}\times4.84\times10^{-6}}{6\times10^{48}}=8.066\times10^{-5}rad/sec^2$$