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

Angular Momentum Conservation: In the absence of an external torque, the net angular momentum of a system remains conserved.

$L = I ω = c o n s t ⇒ I_ 1 ω_ 1 = I_ 2 ω_ 2$

The Moment-of-Inertia of a sphere of mass M and radius R spinning along an axis passing through its centre is :$I = \frac2 5 M R^ 2$

now applying momentum conservation

$\frac2 5 M R^ 2\times\frac{2\pi}{25}= \frac2 5 M (10^{-5}R)^ 2\times w_2$

$w_2=8\pi\times10^8$