Unravelling the Secrets of Neutron Stars

[feedmeister]

Homework Statement

"During most of its lifetime, a star maintains an equilibrium size in which the inward force of gravity on each atom is balanced by an outward pressure force due to the heat of the nuclear reactions in the core. But after all the hydrogen "fuel" is consumed by nuclear fusion, the pressure force drops and the star undergoes a gravitational collapse until it becomes a neutron star. In a neutron star, the electrons and protons of the atoms are squeezed together by gravity until they fuse into neutrons. Neutron stars spin very rapidly and emit intense pulses of radio and light waves, one pulse per rotation. These "pulsing stars" were discovered in the 1960s and are called pulsars."

A star with the mass (2.0 x 10^30 kg) and size (R = 3.5 x 10^8 m) of our sun rotates once every 32.0 days. After undergoing gravitational collapse, the star forms a pulsar that is observed by astronomers to emit radio pulses every 0.200 s. By treating the neutron star as a solid sphere, deduce its radius.

What is the speed of a point on the equator of the neutron star? Your answer will be somewhat too large because a star cannot be accurately modeled as a solid sphere.

Homework Equations

I have no idea of which equations to use.

The Attempt at a Solution

I am completely lost and I don't know how to approach this problem. Can anyone help me?

Thanks,

 

[Bill Foster]

Conservation of angular momentum comes to mind.

$$L_1=I_1\omega_1=L_2=I_2\omega_2$$

Since the problem is talking about periods, then use this:

$$\omega=\frac{2\pi}{T}$$

Also, for a sphere:

$$I = \frac{2 m r^2}{5}$$

You've got everything you need to solve for the radius now.

 

[feedmeister]

Hey Bill,

Thanks a lot!

 

[feedmeister]

Hey,

I got the radius, but how do I get the velocity? I tried L=rmv

Thanks

 

[feedmeister]

Oh I figured it out, it's just v=r*omega

Thanks for the help. I really appreciate it!

 

[nakyong]

Hey, I'm having trouble with this problem as well and I still haven't been able to find the radius. I tried using mr^2 to find the moment of inertia, and then substituting the value into I = (2mr^2/5) to find the radius but it was incorrect. Can anyone help?

 

[Erwin Kreyszig]

Hey, I'm having trouble with this problem as well and I still haven't been able to find the radius. I tried using mr^2 to find the moment of inertia, and then substituting the value into I = (2mr^2/5) to find the radius but it was incorrect. Can anyone help?

Are you using the conservation of momentum?
Find the initial momentum of the star before collapse, then use the conservation to give you a value of I_2 (after the collapse) then you have everything you need.

 

[nakyong]

I'm still confused...doesn't conservation of angular momentum state that L_i = L_f?
Would I need to find I_1 from 2mr^2/5 and w_1 from 2pi/T and set that equal to I_2*w_2to solve for I_2? Wouldn't that just give me the same value for the initial moment of inertia since the w values are the same? or would the period change for 2pi/T?

 

[nakyong]

anyone?

 

[nakyong]

Nevermind guys, I got it now. I was making a stupid mistake. Thanks for all the help!

 

[Nadialy]

Oh I figured it out, it's just v=r*omega

Thanks for the help. I really appreciate it!

Thank you, I was having a hard time figuring that out myself.