# Angular momentum after elastic collision

If two balls collide (elastically) and there is no friction between them, will their angular momentum change after the collision?

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No. Without friction, the forces during the collision are applied exclusively through their centres of mass - hence there is no torque and hence the angular momentum cannot change. Wikipedia has a force diagram that illustrates what I mean: upload.wikimedia.org/wikipedia/commons/2/2c/… – Martin Ender May 5 '13 at 20:07
It doesn't even matter if energy is conserved. A sufficient condition for angular momentum conservation is that the net external torque on the system of colliding particles is zero. – joshphysics May 5 '13 at 20:36
@joshphysics but in the presence of friction angular momentum might be transferred between the two – Martin Ender May 5 '13 at 21:12
@m.buettner That's certainly true. The question refers to "their angular momentum" which I interpreted to mean the angular momentum of the system consisting of both balls. If that's not the case, then my comment is irrelevant. – joshphysics May 6 '13 at 0:04
@m.buettner that (your first comment) should be an answer :-) – David Z May 6 '13 at 4:13

Without friction, the forces during the collision (glancing or head-on) are applied exclusively through their centres of mass. (Illustration available on Wikipedia.)

The torque is given by $\tau=\mathbf r \times \mathbf F$ - but if the forces are applied through the centre of mass, then $\mathbf r$ and $\mathbf F$ are parallel, and hence $\tau=0$.

Without a torque, angular momentum cannot change (because $\frac{\text{d}L}{\text{d}t}=\tau$), so that each ball will keep its angular momentum.

With friction, depending on the relative movement of the balls' surfaces during the collision, there could be a tangential component of the force, which would cause a torque on each ball. Therefore, angular momentum could be transferred. However, as joshphysics mentioned in a comment, the total angular momentum of the system would still be conserved, as there is no external net torque.

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