Neutron star's angular velocity

• MAPgirl23
In summary: You are then given a value for I1I1 and you can calculate I2.In summary, the conversation discusses the concept of a neutron star, which is an extremely dense object made mostly of neutrons that can form under certain circumstances. The density of a neutron star is approximately 10^14 times greater than that of ordinary solid matter. The conversation then presents a problem to find the angular speed of a neutron star, given its initial and final radii, and the assumption that its mass and angular momentum remain constant before and after collapse. Using the formula for angular momentum and the ratio of moments of inertia, the angular speed of the neutron star is calculated to be 4632 rad/s. However, it is noted that the mass
MAPgirl23
Under some circumstances, a star can collapse into an extremely dense
object made mostly of neutrons and called a neutron star. The density of a
neutron star is roughly 10^14 times as great as that of ordinary solid
matter. Suppose we represent the star as a uniform, solid, rigid sphere,
both before and after the collapse. The stars initial radius was 7.0 x
10^5 km (comparable to our sun); its final radius is 16 km.

If the original star rotated once in 30 days, find the angular speed of
-------------------------------------------------------------------

** I think you need to make two assumptions to answer this question. The first assumption is that the mass of the star is the same after collapse as before. The second assumption is that the angular momentum of the star is the same after the collapse as before (angular momentum is conserved, but if the star had, for example, ejected matter during its collapse, the ejecta could have carried away some of its angular momentum).

If the moments of interia of the sphere before and after collapse are I_1 and I_2 respectively, and its angular speeds before and after colapse are w_1 and w_2 then from our second assumption we have:

(I_1)(w_1) = (I_2)(w_2)
=> w_2 = (I_1)(w_1)/(I_2)

You are given w_1 (you are are told that the star rotates once in 30 days before the collapse). And although you do not know I_1 and I_2 directly, you can find their ratio, because each one is proportional to the mass of the star and the square of its radius. From our first assumption the mass of the star is constant, so

(I_1)/(I_2) = (R_1)^2/(R_2)^2

where R_1 is the radius of the start before collapse, and R_2 is the radius after collapse. So

w_2 = (w_1)(R_1)^2/(R_2)^2

now using my logic I got
(R_1)^2/(R_2)^2 = (7.0 x 10^5)^2/(16)^2 = 1.914 x 10^9
w_1 = 1 rotation/2.592 x 10^6 sec = 3.85 x 10^-7

so: If the original star rotated once in 30 days, find the angular speed of the neutron star. 738.4 rad/s which was wrong.

What did I do wrong?

MAPgirl23 said:
w_1 = 1 rotation/2.592 x 10^6 sec = 3.85 x 10^-7

This bit is where you've gone wrong. It should be:

$$\omega_{1} = \frac{2\pi}{T}$$, where T is your orbital period, ie 2.592 x 10^6 s.

MAPgirl23 said:
. The density of a
neutron star is roughly 10^14 times as great as that of ordinary solid
matter

Shouldn't you use the above information below?

MAPgirl23 said:
(I_1)/(I_2) = (R_1)^2/(R_2)^2

MAPgirl23 said:
Under some circumstances, a star can collapse into an extremely dense
object made mostly of neutrons and called a neutron star. The density of a
neutron star is roughly 10^14 times as great as that of ordinary solid
matter. Suppose we represent the star as a uniform, solid, rigid sphere,
both before and after the collapse. The stars initial radius was 7.0 x
10^5 km (comparable to our sun); its final radius is 16 km.

If the original star rotated once in 30 days, find the angular speed of
-------------------------------------------------------------------

** I think you need to make two assumptions to answer this question. The first assumption is that the mass of the star is the same after collapse as before. The second assumption is that the angular momentum of the star is the same after the collapse as before (angular momentum is conserved, but if the star had, for example, ejected matter during its collapse, the ejecta could have carried away some of its angular momentum).

If the moments of interia of the sphere before and after collapse are I_1 and I_2 respectively, and its angular speeds before and after colapse are w_1 and w_2 then from our second assumption we have:

(I_1)(w_1) = (I_2)(w_2)
=> w_2 = (I_1)(w_1)/(I_2)

You are given w_1 (you are are told that the star rotates once in 30 days before the collapse). And although you do not know I_1 and I_2 directly, you can find their ratio, because each one is proportional to the mass of the star and the square of its radius. From our first assumption the mass of the star is constant, so

(I_1)/(I_2) = (R_1)^2/(R_2)^2

where R_1 is the radius of the start before collapse, and R_2 is the radius after collapse. So

w_2 = (w_1)(R_1)^2/(R_2)^2

now using my logic I got
(R_1)^2/(R_2)^2 = (7.0 x 10^5)^2/(16)^2 = 1.914 x 10^9
w_1 = 1 rotation/2.592 x 10^6 sec = 3.85 x 10^-7

so: If the original star rotated once in 30 days, find the angular speed of the neutron star. 738.4 rad/s which was wrong.

What did I do wrong?

I see where you went wrong. You got the right answer, but not the right units. You have 1 revolution/sec... multiply your answer by 2pi...

Last edited:
Thanks, I see what I did.

Wait a minute. How can you say that the mass of the star is conserved? What happened to all the protons (and the electrons) in the star?

Initially you have M1=[4/3(pi)(r_1)^3] X (D1) and M2=[4/3(pi)(r_2)^3] X (D2) .
Since the ratio D1/D2 is given, by substituting the above values, you can get the ratio
I1/I2.

1. What is a neutron star's angular velocity?

A neutron star's angular velocity refers to the rate at which a neutron star rotates on its axis. It is typically measured in rotations per second.

2. How is a neutron star's angular velocity determined?

A neutron star's angular velocity can be determined by measuring the periodic variations in its electromagnetic radiation or by observing the Doppler shifts of its spectral lines.

3. What is the fastest known neutron star's angular velocity?

The fastest known neutron star's angular velocity is about 716 rotations per second, which is equivalent to a rotational period of 1.4 milliseconds. This star is known as PSR J1748-2446ad.

4. Can a neutron star's angular velocity change over time?

Yes, a neutron star's angular velocity can change over time due to a phenomenon known as glitching. This is when the star's rotation suddenly speeds up, followed by a gradual decrease back to its normal rotation rate.

5. How does a neutron star's angular velocity affect its properties?

A neutron star's angular velocity is directly related to its size and mass. The faster the star rotates, the smaller and more massive it is likely to be. It also affects the strength of its magnetic field and the amount of energy it emits in the form of X-rays and gamma rays.

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