Only rotating bodies have angular momentum

[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?

 

[cmb]

Only rotating bodies have angular momentum?

Is this statement false?

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

 

[sinjan.j]

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

 

[Doc Al]

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

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.

 

[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.

 

[JHamm]

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

 

[Drakkith]

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.

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

 

[cmb]

An object traveling in a straight line can have angular momentum if it is moving at some perpendicular from a fixed point or line.

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.)

 

[A.T.]

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

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)

 

[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 doesn't this also show the body will have angular momentum?

 

[fbs7]

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.

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

r = r_o + v_ot
p = mv_o

so L = (r_o + v_ot) x (mv_o) = mr_o x v_o = constant

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