When to use conservation of angular momentum

[henry3369]

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 8.0×10 5km (comparable to our sun); its final radius is 18km.

Homework Equations

Conservation of momentum

The Attempt at a Solution

The solution to this problem is obtained using conservation of angular momentum. I understand how to solve it, but I'm not sure how I would have figured out to use conservation of angular momentum without looking at the solution. For linear momentum it was easy because usually whenever objects collided, the problems usually dealt with conservation of linear momentum. In this problem, one star collapses with no interaction with any other objects.

 

[SteamKing]

It's not clear, based on the information given in the OP, that angular momentum would be a consideration, unless you were given an angular velocity of the star prior to its collapse. It seems like a critical piece of the problem has been omitted from the OP, namely, what the problem was, i.e., what are you supposed to solve.

Have you provided the entire text of the problem statement as it appeared originally?

 

[haruspex]

I feel you're approaching this from the wrong end. You should always look to see which conservation laws might be useful in a dynamics question, discounting those for which preconditions are not met, or which are clearly of no help. In the case you cite, linear momentum won't help, and mechanical energy is not conserved. That only leaves angular momentum.

 

[henry3369]

It's not clear, based on the information given in the OP, that angular momentum would be a consideration, unless you were given an angular velocity of the star prior to its collapse. It seems like a critical piece of the problem has been omitted from the OP, namely, what the problem was, i.e., what are you supposed to solve.

Have you provided the entire text of the problem statement as it appeared originally?

Sorry, I forgot a line of the problem:
If the original star rotated once in 30 days, find the angular speed of the neutron star.
I already found the initial velocity with this information.

 

[henry3369]

I feel you're approaching this from the wrong end. You should always look to see which conservation laws might be useful in a dynamics question, discounting those for which preconditions are not met, or which are clearly of no help. In the case you cite, linear momentum won't help, and mechanical energy is not conserved. That only leaves angular momentum.

How would I know from the information given that mechanical energy is not conserved?

 

[SteamKing]

How would I know from the information given that mechanical energy is not conserved?

I'm not aware of a Law of the Conservation of Mechanical Energy.

In the case of a collapsing star, what mechanical energy would be conserved?

 

[henry3369]

I'm not aware of a Law of the Conservation of Mechanical Energy.

In the case of a collapsing star, what mechanical energy would be conserved?

I'm not sure what would be conserved in a collapsing star, but, in a situation where two objects collide elastically, isn't energy conserved?

 

[SteamKing]

I'm not sure what would be conserved in a collapsing star, but, in a situation where two objects collide elastically, isn't energy conserved?

No, energy is not conserved, but momentum is.

 

[henry3369]

No, energy is not conserved, but momentum is.

I thought that energy is conserved in elastic collisions while energy is lost during inelastic collisions? Isn't that what differentiates between the types of collisions?

 

[SteamKing]

I thought that energy is conserved in elastic collisions while energy is lost during inelastic collisions? Isn't that what differentiates between the types of collisions?

That's why there is no Law of Conservation of Energy (Mechanical or Kinetic). Different things happen to a body's energy depending on the type of collision.

http://en.wikipedia.org/wiki/Collision

 

[haruspex]

I thought that energy is conserved in elastic collisions while energy is lost during inelastic collisions? Isn't that what differentiates between the types of collisions?

Total energy is always conserved, but we consider the random motion of particles in an assemblage to be thermal energy, not mechanical energy. So while the collisions of particles may be elastic, the kinetic energy of the body as a unit can decline.