# Is angular momentum completely independent from linear momentum

1. Feb 7, 2013

### NANDHU001

Is it possible to derive ideas of angular momentum form linear momentum. Can linear momentum and calculus be used to derive ideas of angular momentum.

2. Feb 7, 2013

### lurflurf

I take it you are talking about classical mechanics?

$$L=r \times p$$
where
L is angular momentum
r is position vector
p is linear momentum

So linear and angular momentum are related. They are each conserved. If we have only rigid objects all the angular momentum follows from linear momentum and we can use either momentum according to convenience. If we have bendy objects they can store angular momentum. For example if we had a paddle wheel and we put it in a pot of non-Newtonian porridge it may appear as if angular momentum is not conserved, but in fact it is, the porridge has stored some angular momentum that must be accounted for.

3. Feb 7, 2013

### phion

Sure, a constant horizontal force applied tangentially about an axis of rotation would produce the revolutions per second expressed, preferably, in radians per second.

If you want to find out the moments of inertia, you'd need information about the density of, say, a uniform hollow cylinder about an axis, inner and outer radius, and a length. With that information you can use calculus.

Using integration, you can show the angular momentum of a body expressed as two parts, one from the body's center of mass and one from the motion of the body with respect to its center of mass.