Simple 2D collision formula developments

In summary: Sorry, I sort of lost you. I am yet to have studied momentum, and I tried to understand momentum from guides I have read. Could you just give me a finished formula? I do not necessarily need to thoroughly understand the way it works, I just need the finished formula.
  • #1
AdamAlon
3
0
Hi everybody,
I am currently working on a small computer programming project, and was wondering if you could give me hand.

Say I have two simple, identical balls moving in different speeds and angles towards each other. They hit each other elastically, and weigh exactly the same.
The location of their centers is also a given (see diagram for further explanation).

http://img12.imageshack.us/img12/1108/question.png [Broken]

All the data is according to the diagram (which is completely general).
Can I tell through some sort of formula developments what their new speeds (size+angle) will be, after they collide? (As in U1=?, U2=?, newA1=?, newA2=?)

I tried figuring it out myself but got mixed-up and lost. Hopefully you might be able to help me :-)

Thanks a lot,

Adam
 
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  • #2
Oh sure. I actually had to do this myself for a computer game we made for a class project. I don't know the equations but you can get a simple closed form expression for it. I'm sure if you do enough searching on the web or through textbooks you will find out what it is. Of course in the end you could always derive it.
 
  • #3
Born2bwire said:
Oh sure. I actually had to do this myself for a computer game we made for a class project. I don't know the equations but you can get a simple closed form expression for it. I'm sure if you do enough searching on the web or through textbooks you will find out what it is. Of course in the end you could always derive it.

Yeah, I figured it was rather simple, but I can't seem to find anything of that sort anywhere.
A closed form expression would be fantastic, but I am having a hard time deriving it myself. Thus, I turned to you guys for assistance :)
So, can any of you give me a hand?
 
  • #4
Transform to the center of mass frame in which the total momentum is zero. Forget about the angles and velocities in the original frame for the moment. Just work out the most general case of a collision as seen in the center of mass frame (which is very simple).

Then transform this to a frame in which the initial velocities are arbitrary. You need to do a little algebra to find the angles in that other frame.
 
  • #5
Count Iblis said:
Transform to the center of mass frame in which the total momentum is zero. Forget about the angles and velocities in the original frame for the moment. Just work out the most general case of a collision as seen in the center of mass frame (which is very simple).

Then transform this to a frame in which the initial velocities are arbitrary. You need to do a little algebra to find the angles in that other frame.

Sorry, I sort of lost you. I am yet to have studied momentum, and I tried to understand momentum from guides I have read.
Could you just give me a finished formula? I do not necessarily need to thoroughly understand the way...
 

1. What is a simple 2D collision formula development?

A simple 2D collision formula development is a mathematical equation or set of equations used to calculate the behavior of objects colliding in a two-dimensional space. It takes into account factors such as mass, velocity, and angle of collision to determine the resulting motion of the objects.

2. Why is understanding collision formulas important in 2D games?

Understanding collision formulas is crucial in 2D games because collisions between objects are a fundamental aspect of gameplay. It allows game developers to create realistic and engaging interactions between game elements and ensures that the game mechanics are working as intended.

3. How do you calculate the velocity of objects after a collision?

The velocity of objects after a collision can be calculated using the conservation of momentum formula: m1v1 + m2v2 = m1v1' + m2v2' where m1 and m2 are the masses of the colliding objects, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities after the collision.

4. What is the difference between elastic and inelastic collisions?

Elastic collisions are collisions in which kinetic energy is conserved, meaning that the total energy before and after the collision remains the same. Inelastic collisions, on the other hand, are collisions in which kinetic energy is not conserved and is converted into other forms of energy such as heat or sound.

5. How do you account for rotational motion in 2D collision formulas?

To account for rotational motion in 2D collision formulas, the moment of inertia of the objects must be considered. This value represents an object's resistance to change in rotational motion and can be incorporated into the equations to calculate the angular velocity of the objects after the collision.

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