Angular momentum of a two particle system

[majorbromly]

Homework Statement

I will preface this with: I am in a mechanics class and the professor has made it his duty to explain every single concept in the most high level ways possible, often ignoring necessary basics. As a result, I suck at angular momentum (and plenty of other things)

My best attempt at a drawing from my textbook: http://imgur.com/qUvQE

A is the origin here.

What is are the translational, rotational, and total angular momenta of this system?

After a short time Δt, what is the linear momentum of the system, what is the rotational angular momentum of the system?

Homework Equations

L= r x p
mag(L)=mag(r(perp))*mag(P)
Lrot=Iω

The Attempt at a Solution

One problem I have is I'm unsure how to differentiate between translational and rotational L. I'm mainly confused as to when the general "r cross p" statement applies. I chalk this up to my professor being a string theorist that cannot teach all that well.

I've tried setting up a center of mass, and attempted to solve for L using a perpendicular r of h+1/2d, and a momentum using the center of mass velocity. So, L comes out to -((h+1/2d)*(mvcom))...I would assume this is a total angular momentum?

As you can see I'm a little lost, and I would appreciate any help greatly!

 

[grzz]

Note that given a particle of mass m moving with velocity v at some distance from a point P, then 'angular momentum' of this particle about point P can also be interpreted as the 'moment of linear momentum' of the particle about point P.

 

[majorbromly]

I'm sorry, but I'm not quite sure I understand what you mean, and my google searches haven't helped. Do you think you can try to clarify?


Also, one thing I forgot to mention is that the line between the two masses is a physical rod with length d.

 

[Doc Al]

One problem I have is I'm unsure how to differentiate between translational and rotational L.

One way to put it: The total angular momentum is the angular momentum of the system about the center of mass (the rotational angular momentum) plus the angular momentum of the center of mass (the translational angular momentum).

Start by finding the motion of the center of mass.

 

[asteriatic]

Angular momentum is a fundamental concept in physics that describes the rotational motion of a system. In a two particle system, the angular momentum is the product of the distance between the particles and their individual momenta. This can be represented as L = r x p, where r is the distance vector between the particles and p is the momentum vector of each particle.

In this system, there are both translational and rotational components to the angular momentum. The translational angular momentum is the product of the total mass of the system and its velocity, while the rotational angular momentum is the product of the moment of inertia and the angular velocity (Lrot = Iω).

To determine the translational and rotational angular momenta of the system, you would need to calculate the distance between the particles, their individual momenta, and the moment of inertia of the system. The total angular momentum would be the sum of these two components.

After a short time Δt, the linear momentum of the system would change due to the particles' motion, while the rotational angular momentum would remain constant unless there is an external torque acting on the system. Using the equations of motion, you can calculate the new linear momentum and determine the change in rotational angular momentum, if any.

It is important to understand the basics of angular momentum before diving into more complex concepts. I suggest reviewing the fundamentals and practicing with simpler systems before tackling more advanced problems. Remember, practice makes perfect. Good luck!