Predicting Angular Momentum in Elastic Collisions

[Aidman]

Hi,

Is it possible to predict the “angular consequences” of an elastic collision? Let’s say we have two rectangular objects, A and B. Their original angular velocities and linear velocities, as well as mass and moment of inertia, are all known. Is it than possible to predict their angular velocities after they hit, knowing the collision-point? If so then how, because I can only figure out one equation, where both unknown angular velocities are stated:

I[A] * w[A](before) + I * w(before) = I[A] * w[A](after) + I * w(after)
where as w(after) and w[A](after) are unknown... any ideas?

 

[rocketcity]

What angle the two bodies will go flying off at after the collision is highly dependent on how they strike. Think about lining up a pool shot: the six ball is stationary, and the cue ball is traveling due north towards it at a certain speed. Depending on where on the six ball you hit it, the resulting velocity pairs may have directions of (for six ball and cue ball, respectively:) north and south, northwest and northeast, northeast and southwest, etc.

In a frictionless situation, I can use conservation of (all three) components of linear momentum to predict the motion of one of the balls after the collision *if I know the motions of BOTH balls before the collision and ONE of the balls after the collision.*

It's also true that you can predict which direction both balls will go in IF you know enough about their geometries and how the collision will occur. For example, I've done problems where you bounce a golf ball off of a bowling ball. By knowing where on the bowling ball it will hit, you can use ray geometry to predict which way it will bounce. Then, as I said above, you could use conservation of momentum to figure out what the bowling ball would do.

P

 

[franznietzsche]

Originally posted by rocketcity
What angle the two bodies will go flying off at after the collision is highly dependent on how they strike. Think about lining up a pool shot: the six ball is stationary, and the cue ball is traveling due north towards it at a certain speed. Depending on where on the six ball you hit it, the resulting velocity pairs may have directions of (for six ball and cue ball, respectively:) north and south, northwest and northeast, northeast and southwest, etc.

In a frictionless situation, I can use conservation of (all three) components of linear momentum to predict the motion of one of the balls after the collision *if I know the motions of BOTH balls before the collision and ONE of the balls after the collision.*

It's also true that you can predict which direction both balls will go in IF you know enough about their geometries and how the collision will occur. For example, I've done problems where you bounce a golf ball off of a bowling ball. By knowing where on the bowling ball it will hit, you can use ray geometry to predict which way it will bounce. Then, as I said above, you could use conservation of momentum to figure out what the bowling ball would do.

P

Angular=rotational, wrong problem there.

To answer your question Aidman in a system with objects moving in a rotational matter (say two balls being swung on strings) the results of elastic collisions are the same as if the equations were between the poll balls describewd by rocket city. Momentum and Energy are both still conserved. You can use the same equations if you replace mas with moment of inertia, velocity with angular velocity, momentum with angular momentum, et al.