Question

A star with radius R1 = 7.0 x 105 km collapses into a neutron star with radius R2 = 16 km. If the original star rotates once per month, what is the (a) angular speed of the neutron star in revolutions per second, and (b) the period of the rotational motion? Treat the star as a sphere with moment of inertia I = 2/5 MR². You must show all of your work to receive full credit for this problem. (1 month = 30 days, 1 year = 365 days)

Answer 1

a)

Here the large star is collapses internally to the neutron star with smaller radius.

Here the radius of the original star,

the radius of the neutron star,

We have the period of one rotation of the original star or time period of the original star,

So,

So,the angular velocity of the original star,

Here for the collapse of the original star to neutron star,there is no external torqua acting on the system.

So,the angular momentum is conserved here.

Moment of inertia of star,

Here the mass of original star=mass of neutron star=M

So,Moment of inertia of original star,

So,Moment of inertia of neutron star,

Initial angular momentum of the original star,

Fianl angular momentum of the neutron star,

Ie,

Or,

ie,

So,

So,the angular speed in revolutions per seconds=?

Here,

So,

So,the angular speed of the neutron star in revolutions per seconds,

b)

We have the period of the original star,

For the neutron star,

Here we have got the angular velocity of the neutron star, in rev/s,

ie,the angular velocity of neutron star in rad/sec,

angular velocity of neutron star in rad/sec,

We have the time period of neutron star,

So,the time period of the neutron star,