Suppose a star the size of our sun but with mass 80 times as...

Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 9.0 days. If it were to undergo gravitational collapse to a neutron star of radius 12 km, losing $\frac{3}{4}$ of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times. Assume also that the thrownoff mass carries off either $(a)$ no angular momentum, or $(b)$ its proportional share $(\frac{3}{4})$ of the initial angular momentum.

Transcript

00:01 So this problem, one asked to determine the angular speed of the new neutron star for this two situations.

00:08 First, when no angular momentum in the throne of mass, second, when three -fourths of the angular momentum carried by the throne of mass.

00:44 So let's start with situation a.

00:45 When angular momentum in throne of mass, then the angular momentum initial is equal to angular momentum final.

00:54 And we know that angular momentum is the product of the moment of inertia and the angular speed.

01:04 So our equation becomes like this.

01:09 And we know that the moment of inertia for sphere, assuming that the star is in perfectly spear shape, then this equals to 2 over 5x m r square, where m here is the mass of the sphere and r is the radius.

01:29 So our equation become like this.

01:42 So simplifying, isolating the rotational speed or the angular speed of the neutron star, then we have this.

01:59 Note that it was stated in the problem that the mass of the neutron star, i mean, it was stated in the problem that the throne of mass was three -fourths of the original mass.

02:15 Or the initial star lose three ports of its initial mass.

02:19 Then the mass of the neutron star is only one -fourth of the original since three -fourth is loosed.

02:29 Then inserting it in our equation, we have this.

02:44 Then simplifying, the equation becomes like this.

02:52 Note that, it was stated that the initial star has the same size as our sun.

02:57 So its radius is equals to the radius of our sun.

03:01 Then we have the radius of our sun, which is 6 .96 times 10 -0 .8 meter, quantity squared over the given radius of our sun...