Angular momentum

Conservation laws.

This states that the total energy, momentum, and angular momentum remain constant in an isolated system.

We calculate the momentum of a system and we treat the system as one specific system, an isolated system.

Force laws.

And we are back.

I wanted to get more into the subject here so we can look at this online course.

This first course in the physics curriculum introduces classical mechanics, historically a set of core concepts, space, time, mass, force, momentum, torque, and and angular momentum were introduced in classical mechanics in order to solve the most famous physics problem, the motion of the planets.

The principles of mechanics successfully described many other phenomena encountered in the world.

You remember in the world of rotation, we defined something called momentum, which is mass times velocity.

Here, we're going to call something called angular momentum.

It's going to be I times ω.

This I is called the angular So, one extremely important point that you guys should notice is that all the concepts I'm using, like mass and energy, they are the same old concepts that we learned earlier on.

The fact that it's a rotating body doesn't change anything, okay? Kinetic energy still means the same.

This k, though it looks so different, is in fact the ½ mv² of every part of the body So, this L is called angular momentum.

It'll take a while to get used to this, but right now, it's a product of the moment of inertia and the angular velocity.

So now, we are looking for the most important equation in that's going to be equal to some mystery object.

We're going to take a rather simpler version of the rigid body problem, basically the problem of torques and forces in 3-D, but apply it in a very limited context.

The limited context I've set for myself right now is to just What is the analog of τ equals iα when the mass is not moving in the xy plane but just running around all over three dimensions? How do we define torque? How do we define angular momentum in 3D? You'll find that it's not a straightforward extension.

You have to think a little harder.

Let me motivate the problem we have.

I hope you know what that means.

If a force is acting at the point with vector r, measured from some origin, the torque due to that force is r x F.

Now, I'm going to introduce for a single point mass, somewhere here, an angular momentum, the angular momentum.

Previously, angular momentum, iω, is not a vector.

Uh, Martin, one of our regular contributors, has a dark matter he wants to discuss.

Uh, Peter in Sweden is talking angular momentum.

Uh, that is the angular momentum of matter falling into a black hole.

And a real bummer of a question.

We'll tell you all about it on this episode of Space Nuts.

Space Nuts.

Our next question comes from Sweden.

Uh, can matter that falls into a black hole keep its angular momentum and sort of add it to the black hole's angular momentum? Uh, or does matter fall into a black hole, um, or does matter falling into a black hole need to shed its angular momentum or part of it through, uh, radiating energy out into space before it can fall down the hole? If so, why can't a black hole that can retain light and, uh, spaghettify things, pull things in despite their angular momentum and just add the incoming momentum to itself? That comes from Peter in Sweden.