Conservation of Momentum; finding the angular speed of a Neutron star

In summary, a neutron star is a very dense object made mostly of neutrons. The density of a neutron star is roughly 10^{14} times as great as that of ordinary solid matter.
  • #1
Northbysouth
249
2

Homework Statement


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 star's initial radius was 6.0×10^5km (comparable to our sun); its final radius is 16km

If the original star rotated once in 33 days, find the angular speed of the neutron star.
Express your answer using two significant figures and in rad/s

Ri = initial radius
Rf = final radius

Homework Equations


Conservation of Momentum

I = 2/5MR^2

L = Iw

The Attempt at a Solution



I first converted the 1 rev/ 33 days to rad/s

1/33 rev/ day *(2pi)*(1 day/24 hours)*(1hour/60 min)*(1 min/60 sec)
w = 0.000002 rad/s

I = (2/5)*(M)*(Ri^2)*(0.000002) = (2/5)*(M)*(Rf^2)wf

The masses (M) and the 2/5 cancel

3.6x1017 = 2.56x108*wf

wf = 1.40625x109

It says it's wrong. The only thing that I can think of that is wrong is that I did the angular velocity (w) conversion wrong.
 
Last edited:
Physics news on Phys.org
  • #2
Northbysouth said:
I first converted the 1 rev/ 33 days to rad/s

1/33 rev/ day *(2pi)*(1 day/24 hours)*(1hour/60 min)*(1 min/60 sec)
w = 0.000002 rad/s

Hello,
Note that you've only kept 1 significant figure in w. How many sig figs should you have? Also, you might want to use scientific notation for this very small number.

I = (2/5)*(M)*(Ri^2)*(0.000002) = (2/5)*(M)*(Rf^2)wf

I'm sure you meant to type L rather than I at the beginning of the equation.

The masses (M) and the 2/5 cancel

3.6x1017 = 2.56x108*wf

Did you forget to multiply by wi on the left side?
 
  • #3
I think you're right. So I get:
(6x10^8)^2 * 0.000002 = (16000)^2 * wf

wf = 2812.5 rad/s

But my answer is still wrong
 
  • #4
Look's like your method is correct. But I really do think you should include more significant figures in your expression for wi. The number .000002 has only one significant figure. The problem gives data with two significant figures. What do you get for wi expressed to two significant figures? How does this affect your final answer?
 
  • #5
You are correct. I ran the calculation again using the exact value my calculator gave me. wf = 3098.95.

My calculator is a TI-89 and I was used the approximate function to get the answer, which gave me 0.000002. The real value for wi is pi/1425600.
Thank you for your help.
 

1. What is the conservation of momentum?

The conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant, unless an external force is applied.

2. How does this law apply to finding the angular speed of a Neutron star?

The conservation of momentum is applicable to finding the angular speed of a Neutron star because the total momentum of the system (Neutron star) remains constant, even as it rotates.

3. What factors affect the angular speed of a Neutron star?

The angular speed of a Neutron star is affected by its mass, radius, and moment of inertia. As these factors change, the angular speed of the star will also change accordingly.

4. Can the conservation of momentum be used to calculate the exact angular speed of a Neutron star?

No, the conservation of momentum alone cannot be used to calculate the exact angular speed of a Neutron star. Other factors, such as the star's internal structure and external forces, must also be considered in order to determine its precise angular speed.

5. Why is it important to study the angular speed of Neutron stars?

Studying the angular speed of Neutron stars can provide valuable insights into the properties and behavior of these highly dense and unique objects. It can also help us understand the fundamental laws of physics, such as the conservation of momentum, in extreme conditions.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
818
  • Introductory Physics Homework Help
Replies
1
Views
814
  • Introductory Physics Homework Help
Replies
4
Views
784
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
20
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
4K
  • Introductory Physics Homework Help
Replies
5
Views
776
Replies
13
Views
818
Back
Top