# Momentum of a ball

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1. Sep 30, 2015

### CiElBi

I am currently trying to program a simple game in which a ball bounces of a paddle to hit blocks, and the game ends when all the blocks are broken.

However, I know that when the paddle is moving in one direction, when the ball collides with the moving paddle, the ball should bounce of with a change in momentum towards the direction the paddle was heading.

the paddle is not moving towards the ball, only to the right and left, but the paddle has momentum in those directions which transfers to the ball.

My question is what angle and speeds would the ball be reflected at after it collides with the paddle, assuming both have a very low weight, and if there is any formula I could try to base the programming on to make the simulation more accurate.

2. Sep 30, 2015

### nasu

It will depend on the friction between the ball and paddle. If there is no friction, there is no tangential momentum transfer.
If there is friction, you will need to model in detail the collision, to find the contact time and how the normal force changes during this time.
So better neglect friction.

3. Sep 30, 2015

### jbriggs444

You could use a model in which friction is perfect and elastic so that the tangential velocity of the ball at the contact patch is reversed on impact with the paddle.

If you neglect spin, this means that the ball will rebound in a way that will look quite startling. If it hits a motionless paddle coming down and to the right, it will bounce back along the same path -- up and to the left.

If you model spin then you will get behavior like the child's toy that I played with as a child, a "super ball". A super ball is a small, hard rubber ball which bounces with good elasticity (>90%) and has a surface which is sticky enough that it has the above behavior. The contact patch rebounds from the floor with its tangential velocity reversed. The behavior of super balls is visually jarring. If given a spin, it can bounce back and forth on the floor in a series of decreasing parabolic arcs. You may be better off with a model that softens that ideal behavior and therefore looks more natural.

4. Oct 7, 2015

### CiElBi

Hmm, the ball would be something like a ball used in table tennis, and the paddle to have the same friction as a table tennis bat does.
Currently, the code does run do that the ball bounces back without any changes to the velocity other than inverting the numbers, but that is a very predictable pattern.

I guess the best option would be to model spin into it, and have researched a bit and found information such as the Magnus effect for top spin and back spin of the ball through air, but i haven't found much on how the paddle would affect the spin of the ball in the first place. Are there any equations that might be useful in this situation i could use?
I'm not sure what equations id need, or if there is not a way to calculate it.