# Only rotating bodies have angular momentum

1. Dec 21, 2011

### sinjan.j

Only rotating bodies have angular momentum?

Is this statement false?

I had read it somewhere that it is false that only rotating bodies have angular momentum,

angular momentum = moment of inertia * angular velocity.

Both deal with rotation. so how is the above statement false?

2. Dec 21, 2011

### cmb

I think you can make it true or false, according to how you define 'rotating bodies'.

3. Dec 21, 2011

### sinjan.j

Yeah even I thought about that point. I just can't think of any other.

4. Dec 21, 2011

### Staff: Mentor

Consider a point mass moving with momentum p. If its position vector is r, then its angular momentum about the origin is L = r X p. (r, p, and L are vectors) Nothing is rotating.

5. Dec 21, 2011

### sinjan.j

I just found out another answer. And I think this was what I was looking for. Thank you all.

suppose you have a ball moving in a straight line toward a door. The door is hinged on one side, and the ball is moving toward the other end (the door knob end) of the door. If the door is ajar, when the ball hits the door, it will cause the door to rotate about its hinged axis.

In this case, the moving ball must have had initial angular momentum, because at the end, the door acquired angular momentum when it rotated about its hinged end; since angular momentum is conserved when there are no external torques (and there are no external torques in this example), the ball had initial angular momentum.

An object traveling in a straight line can have angular momentum if it is moving at some perpendicular from a fixed point or line. Here, the ball has angular momentum equal to

L = m v r where m is the balls mass, v is its speed and r is the perpendicular distance between its direction of travel and the hinges.

6. Dec 22, 2011

### JHamm

It does not have to be moving perpendicular to some predefined axis, Doc Al already gave you the answer above.

7. Dec 22, 2011

### Drakkith

Staff Emeritus
The ball hitting the door isn't an external torque?

8. Dec 22, 2011

### cmb

You mean, like some moving objects don't do so wrt a fixed point?

This is all flahh-di-blahh semantics.

You could argue that the ball hitting the door has angular momentum before doing so (about the door hinge), or you could argue that it passes only linear momentum to the door, the consequence of which is that the hinge constrains the door's motion and applies a torque (the reaction at the hinge, wrt the door's CoM) to the door to make it rotate. Take your pick.

Anyhow you like it, there is no argument on the physics, and I do not believe use of these terms are so 'well-defined' in general mathematics for precisely the reason that angular momentum and linear momentum can be chosen wrt whichever axis it is most convenient for you to resolve around. So I'd suggest the issue here is that you are asking a question presuming there to be *an* answer, yet there is not such an answer.

(I would add a few caveats to that, to be more rigorous about such a definition, but are beyond the scope of this thread.)

9. Dec 22, 2011

### A.T.

Not if you treat the ball+door as an isolated system. The angular momentum of that system must be preserved as well. If a system is not rigid you can have:
- Non zero net angular momentum without rotation (as the ball+door shows)
- Rotation with zero net angular momentum (as the falling cat shows)

10. Dec 22, 2011

### nandinitri

isnt it also true tht a body moving in a linear payh wud also have angular velocity(bcoz as the body moves ,taking a point as the origin,we can see tye angle made by it changing)??so doesnt this also show the body will have angular momentum?

11. Dec 22, 2011

### fbs7

It's worth noting that if that's a particle moving at constant speed in a straight line, then

r = ro + vot
p = mvo

so L = (ro + vot) x (mvo) = mro x vo = constant

Therefore that particle has constant angular momentum. Quite curious result, given the "distance" changes, but the velocity doesn't.