Answer to Question #111070 in Mechanics | Relativity for Balogun Raheem

Question

suppose a uniform spherical star of mass M and radius R collapses to a uniform sphere of radius 10^-5 .If the original star had a rotation rate of 1 rev each 25 days(as does the sun) ,what will be the rotation rate of the resulting object

Answer 1

As per the question,

Mass of the spherical star=M

Radius of the spherical star= R

Radius of the other star$=10^{-5}R$

rotational speed of the first star$\omega_1= 1/25 rev/day$

rotational speed of the second star $\omega_2=?$

Now, applying the conservation of angular momentum,

$I_1\omega_1=I_2\omega_2$

$\Rightarrow \omega_2=\dfrac{I_1\omega_1}{I_2}=\dfrac{10^{10}}{25}=4\times 10^8 rev/day$

$\omega_2=4.6\times 10^3 rev/sec$