# Conservation of momentum question

• CuriousInPA
In summary: Externally you get event horizon(s). Inside the event horizon you get a ring singularity. A point singularity only occurs for a non-rotating black hole. In GR, spacetime curvature (the metric) can incorporate angular momentum, so the complete black hole structure can be said to have angular momentum. Inside the horizon, nobody believes the idealized Kerr black hole describes what would really happen. This is outside currently understood physics (IMO).

#### CuriousInPA

Ok, I've been wondering about this question for many years and I don't know whether I just don't understand the basic concepts enough.

If you have a rapidly-spinning neutron star that continues to collapse down to a singularity, what happens to the conservation of angular momentum from the spin? As the circumference of the neutron star approaches zero, what happens to the speed of the spin? Would it actually have to approach c? Would the energy get bled off into some other form?

When I clicked on this link I thought that there might be a 1kg mass in a completely elastic collision with something . Cool question though, sorry I don't know squat about this kinda stuff.

CuriousInPA said:
If you have a rapidly-spinning neutron star that continues to collapse down to a singularity, what happens to the conservation of angular momentum from the spin? As the circumference of the neutron star approaches zero, what happens to the speed of the spin? Would it actually have to approach c? Would the energy get bled off into some other form?
Well, neutron stars do not collapse to a singularity; they typically are about 20km in diameter, with masses on the order of the sun.

http://en.wikipedia.org/wiki/Neutron_star#Rotation

It suggests newborn (i.e. fastest) neutron stars rotate on the order of once per second, which with a circumference of a mere 64km, is quite slow.

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dacruick said:
When I clicked on this link I thought that there might be a 1kg mass in a completely elastic collision with something . Cool question though, sorry I don't know squat about this kinda stuff.

Thanks. Not sure if I've posted this in the right section, though.

DaveC426913 said:
Well, neutrons tars do not collapse to a singularity; they typically are about 20km in diameter, with masses on the order of the sun.

Ok, then if a star is collapsing down past neutron star stage and it was spinning, does that apply?

CuriousInPA said:
Thanks. Not sure if I've posted this in the right section, though.

You definitely did, I didn't even read the category

A black hole can have angular momentum and charge. In fact, externally, once stabilized, a black hole is fully characterized by mass, charge, and angular momentum.

PAllen said:
A black hole can have angular momentum and charge. In fact, externally, once stabilized, a black hole is fully characterized by mass, charge, and angular momentum.

Cool. So, as the circumference of the black hole shrinks, the rate of spin increases, correct? If the circumference approaches zero, what happens to the rate of spin? Would this have any effect on a practical limit to how small a black hole could become?

CuriousInPA said:
Cool. So, as the circumference of the black hole shrinks, the rate of spin increases, correct? If the circumference approaches zero, what happens to the rate of spin? Would this have any effect on a practical limit to how small a black hole could become?

Externally you get event horizon(s). Inside the event horizon you get a ring singularity. A point singularity only occurs for a non-rotating black hole. In GR, spacetime curvature (the metric) can incorporate angular momentum, so the complete black hole structure can be said to have angular momentum. Inside the horizon, nobody believes the idealized Kerr black hole describes what would really happen. This is outside currently understood physics (IMO).

## 1. What is the conservation of momentum?

The conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on the system.

## 2. What is the equation for conservation of momentum?

The equation for conservation of momentum is: Σpi = Σpf, where pi represents the initial momentum and pf represents the final momentum of the system.

## 3. What are some real-life examples of conservation of momentum?

Some examples include a billiard ball colliding with another ball, a rocket launching into space, or a person jumping off a diving board.

## 4. How does conservation of momentum relate to Newton's Third Law?

Conservation of momentum is directly related to Newton's Third Law, which states that for every action, there is an equal and opposite reaction. This means that when two objects collide, the momentum lost by one object is gained by the other, resulting in a constant total momentum.

## 5. Are there any exceptions to the conservation of momentum?

In classical mechanics, conservation of momentum holds true in all situations. However, in certain scenarios, such as at the quantum level or in the presence of strong gravitational forces, conservation of momentum may not apply and other factors must be taken into account.