# Angular momentum transfer in collision between two smooth bodies

I know that conservation of angular momentum says that the total angular momentum is time invariant in absence of external forces.

So say you consider two identical smooth spheres and you make the first sphere strike the second, how would you know if the first transferred any angular momentum into the second without observing it?

Say inertia of each ball is $$I$$ and say angular velocity of first ball is $$\omega_a$$ and second ball is stationary

$$I \omega_a = I \omega '_{a} + I\omega'_{b}$$ or,

$$\omega_a =\omega'_{a} + \omega'_{b}$$

where the primes denote final angular velocity.

Is there any more deductions I can make about the system (since both balls are identical and smooth) or is this it?

• What would cause the bodies to exchange angular momentum? There has to be a contact torque between them. If they are smooth it would seem that they would not exchange spin during the collision.
– user196418
Apr 21, 2020 at 17:31
• Oh so let me get this straight for an exchange to occur in angular momentum the bodies have to make a rough contact? Then would there be momentum transfer? Suppose there is and speed of first ball reduces , wouldn't it's rotation also reduce? or would it start slipping motion? Apr 21, 2020 at 17:37
• These are spheres, identical spheres. When they collide the only other contact force will be the normal force. We are assuming ideal hard spheres (right?). So the impact force will act through the center of mass of each. There is nothing to cause a torque.
– user196418
Apr 21, 2020 at 17:48
• @ggcg This time you beat me to it :-D... yes, only friction between the spheres can provide a torque to change their angular momentum, in accordance with the rotational version of N2L. Apr 21, 2020 at 18:10
• @DDD4C4U Conservation laws are $sometimes$ enough to determine final states in a collision process but they are not sufficient to demonstrate that a process happens. For example, in a two body elastic collision one possible solution is $v_{1f} = v_{1i}$ and $v_{2f} = v_{2i}$. We exclude this because it means that the two "solid" balls passed through each other. We need to invoke some knowledge of the internal contact forces to complete the problem.
– user196418
Apr 21, 2020 at 18:21