# Elastic collision questions

1. May 30, 2009

### luckis11

When two equal masses collide without having any rotational velocity before the collision, and they do attain some rotational velocity after the collision, then do we subtract the rotational momentum from the linear momemtum which is given by the known equations, or is the rotational momentum procuded in addition to the linear momentum?

2. May 30, 2009

### cepheid

Staff Emeritus
You can't subtract two physical quantities that don't have the same dimensions (this makes no more sense than subtracting a time from a length). I believe that the answer is that angular momentum is conserved separately. Since there was none to begin with, the angular momenta of the two masses must sum to zero.

Linear momentum, which describes the translational motion of the centre of mass of each object, is also conserved. Conservation of (linear) momentum would be applied to this problem in the normal way in order to obtain the speed and direction of translation of the centre of mass of each object.

3. May 30, 2009

### luckis11

Is this just your opinion or an established theory of physics based on logic? If it is established, has it also been prooven experimentally?

4. May 30, 2009

### cepheid

Staff Emeritus
How about "classical mechanics?" Have you heard of Newton's second and third laws? I think that conservation of momentum follows quite readily from them. The bottom line is that if these two objects collide, then in the absence of any external forces, momentum is conserved. In the absence of any external torques, angular momentum is also conserved. Yes I'm sure it has been proven experimentally/put to practical use (flywheels and innumerable other things) countless times in the past four centuries.

5. May 30, 2009

### luckis11

Any links clarifying this with an example?

Last edited: May 30, 2009
6. May 30, 2009

### Staff: Mentor

7. May 30, 2009

### luckis11

I just found strange that when a moving ball having a velocity u at the axis of x, hits a still ball non-metopically, then after the collision two equal momentums are born out of zero at the axis of y, that were not existent before the collision. "But this does not violate the conservation of momentum because they have the opposite direction".

And you are saying that in this case, not only these two mementums at the axis of y are born out of zero, but also angular, rotational momentums are born out of zero. Have I got it right?

8. May 31, 2009

### Majcah

If the two objects are spherical in shape and collide in such a fashion as to result in return angles that differ from their approach, then I believe that the nature of the material can produce angular momentum due to rolling friction.

Last edited: May 31, 2009
9. May 31, 2009

### luckis11

Isn't the angular momentum of the still ball (at least also) caused by the fact that during the collision, one part of the still ball attains part of the linear velocity of the moving ball, whereas the other part of the still ball is not? Then it also seems reasonable that the angular momentum is subtracted from the linear momentum, i.e. some linear momentum became angular. Both of the two different answers seem reasonable. If I could handle all the seeming logical complications of the problem, I wouldn't ask which answer is the correct one.

Actually I only want the answer of classical physics. What happens in reality, is very doubtful for me. For example, I doubt that two opposite momentums can be born out of zero. And if (as it seems) this has indeed been prooven experimentally, it is very possible that rest momentums of the balls became linear momentums of the balls.

Last edited: May 31, 2009
10. Jun 3, 2009

### luckis11

When a moving ball hits a still ball of equal mass obliquely, having a velocity u before the collision at the axis of x, then the sum of the moduluses (absolute values) of the two resultant momentums of the two balls after the collision is greater than the sum of the moduluses of the resultant momentums of the two balls before the collision. Does this increase of the sum of the moduluses of momentums (comparing the before and the after the collision sum), happen only in the case that one of the two balls is still before the collision, or does it also happen when both balls are moving before the collision?

Last edited: Jun 3, 2009
11. Jun 3, 2009

### cepheid

Staff Emeritus
The best way to think about it is in terms of torques. Do you know what the relationship between torque and angular momentum is? If you do, you will realize that the only way for the still ball to gain some angular momentum is if there is a net torque exerted upon it. This will happen if the moving ball hits it off-centre, meaning that there is a *force* acting on the still ball a certain *distance* away from the centre of mass. This force acting at a distance produces a net torque around the centre of mass and sets the ball spinning.

Why does this seem reasonable? You haven't really explained that. Remember what I said about how adding or subtracting physical quantities that have different dimensions is meaningless?

What two answers are you referring to? It's not clear in your post.

What??? Why? If the predictions of classical physics had not been borne out by experiment, then it would have been rejected in favour of something that did explain what we observe in reality. But this did not happen, because as far as we know, there is a well-defined range of energies and length scales over which classical mechanics is perfectly applicable and describes nature with great precision. Look at the success of Newtonian gravitation in explaining the motions of the planets, for example. There is no logical reason for you to doubt that what classical mechanics says about colliding balls should be any different from "reality."

Why not??? They ADD UP to zero, don't they? Remember, momentum is a VECTOR quantity.

Here you are not using standard terminology. What do you mean by "rest momentums?" As far as I know this term is not meaningful.

12. Jun 3, 2009

### luckis11

Forget about it all, it is needed to say a lot to explain what I mean. What is the answer to the question of my previous post?

13. Jun 3, 2009

### Staff: Mentor

Are you saying that the total momentum after the collision is greater than before the collision? If so, that's incorrect.

Momentum is conserved; the total quantity of momentum (which is a vector) does not change.

Note that momentum is not simply mass*speed, but mass*velocity. The direction makes a big difference!

14. Jun 3, 2009

### Staff: Mentor

Why should you find this strange. It happens all the time. In billiards, with rockets, in car crashes, etc. That is exactly how momentum works and it is clearly demonstrated all the time in nature.

Yes. If one object exerts a clockwise torque then the other object exerts a counter-clockwise torque. The sum of the two torques is 0 and therefore angular momentum is conserved. This follows from Newton's 3rd law.

15. Jun 3, 2009

### cepheid

Staff Emeritus
Okay, as requested, I will look only at this post:

Did you make up this statement, or is it a quote from somewhere?

The total quantity of momentum does not increase. That is the whole point. In every scenario, momentum is *conserved*, and, in the case of an elastic collision, energy is conserved. These two facts are what allow you to determine what will happen.

If one ball is still, and the other ball is moving in a straight line along the x axis, then there was initially zero momentum along the y axis before the collision. That is why the y-components of the momenta after the collision have to be equal in magnitude and opposite in direction, so that momentum will be conserved.

If both balls initially have some momentum in the y-direction, then the final y-momenta do not have to add up to zero. They just have to add up to the same value as the initial y-momenta (again, momentum is conserved).

16. Jun 3, 2009

### luckis11

Ok, substitute the word "quantity" with "absolute values".

Last edited: Jun 3, 2009
17. Jun 3, 2009

### Staff: Mentor

Please rephrase your question clearly. Don't use the term "momentum" if that's not what you mean.

18. Jun 3, 2009

### luckis11

When a moving ball hits a still ball of equal mass obliquely, having a velocity u before the collision at the axis of x, then the sum of the moduluses (absolute values) of the two resultant linear momentums of the two balls after the collision is greater than the sum of the moduluses of the resultant linear momentums of the two balls before the collision. Does this increase of the sum of the moduluses of linear momentums (comparing the before and the after the collision sum), happen only in the case that one of the two balls is still before the collision, or does it also happen when both balls are moving before the collision?

Last edited: Jun 3, 2009
19. Jun 3, 2009

### Staff: Mentor

The sum of the moduluses of the momenta can increase or decrease or stay the same depending on the details of the interaction, you cannot make any general statements about it. The sum of the moduluses of the momenta is not a useful quantity and is not conserved. Momentum is a vector quantity and must be treated as such.

20. Jun 3, 2009

### luckis11

You did not answer the question.

Also, in which cases this sum is reduced after the collision instead of increased? I cannot find any case that it is reduced (always refering to perfectly elastic collisions).