angular momentum

[captainjack2000]

1. The problem statement, all variables and given/known data
I am trying to write a short speech about angular momentum - aimed at kids leaving school and going on to university. I have started with a breif description of linear momentum, definition of vector, and them the fact that linear momentum is analogous to angular momentum and linear velocity is the counterpart of angular velocity. I then say that an object does not need to be rotating about an origin to have angular momentum. Is this right. Does it just have to been moving at a changing angle wrt to a point? If I then say L=m(rxv) is that the best way to explain angular momentum?
HELP


2. Relevant equations



3. The attempt at a solution

[buffordboy23]

I then say that an object does not need to be rotating about an origin to have angular momentum. Is this right. Does it just have to been moving at a changing angle wrt to a point? If I then say L=m(rxv) is that the best way to explain angular momentum?
HELP

Angular momentum is defined as the cross product of the position vector and linear momentum of a particle as you stated:

\vec{L} = \vec{r} \times \vec{p}

The angular momentum of a particle is dependent upon where we place the origin of our system; as the origin is moved closer to the particle, the magnitude of \vec{r} becomes smaller, and as a consequence, the magnitude of the angular momentum becomes smaller as well for the same linear momentum \vec{p} . An alternative definition is

L = rpsin\theta

where \theta is the angle between the position and linear momentum vectors.

Yes, you are right the object does not necessarily need to be rotating about the origin to have angular momentum.

What is the nature of your class? Have they any knowledge of angular momentum, or even linear momentum? Please don't take offense, but it appears that you want to give a comprehensive yet short discussion on these topics and with some mathematical rigor. Will the kids need these equations in the near future? Perhaps, intuitive examples from everyday experience will be better oriented towards your audience? Good luck.

[captainjack2000]

The class has knowledge up to higher physics but we are asked to presume that they need a short refresher on everything. We only have less than 15 mins for this! I have already giving a brief introduction to linear momentum and vector cross products. The main focus of this is angular momentum itself. I do agree that talking of everyday applications is essential, but I need to explain angular momentum firstly.

why doesn't the object need to be rotating?

[buffordboy23]

why doesn't the object need to be rotating?

It's inherent in the definition. Generally, angular momentum is associated with rotating systems, such as a planet revolving around a star; you can actually derive Kepler's Second Law using angular momentum conservation. Let me know if you need more detail about anything, and I'll try to answer any specific questions.