Question

In: Physics

Suppose a star the size of our Sun, but with mass 5.0 times as great, were...

Suppose a star the size of our Sun, but with mass 5.0 times as great, were rotating at a speed of 1.0 revolution every 18 days. If it were to undergo gravitational collapse to a neutron star of radius 14 km , losing three-quarters of its mass in the process, what would its rotation speed be? Assume also that the thrown- off mass carries off either

part a. no angular momentum

part b. its proportional share three-quarters of the initial angular momentum

Expert Solution

The mas of the star is

The radius of the star is

The moment of inertia of the star is

The period of revolution is

So, the angular speed of the star is

So, the initial angular momentum of the star is

PART A: When no momentum is lost

The radius of the collapsed star is

The mass of the collapsed star is

The moment of inertia of the collapsed star is

The angular momentum of the collapsed star is

The conservation of angular momentum gives us

So, the new rotational speed of the collapsed star is 39887 rad/s.

PART B: When three-quarters of the momentum is lost

The radius of the collapsed star is

The mass of the collapsed star is

The moment of inertia of the collapsed star is

The angular momentum of the collapsed star is

The three-quarter of the initial angular momentum is lost.

So, the conservation of angular momentum gives us

So, the new rotational speed of the collapsed star is 9972 rad/s.

genius_generous answered 1 month ago

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