3D elastic collisions of spheres: angular momentum

In summary, the conversation is about modeling collisions between spheres in a 3D space combat game. The speaker has figured out how to calculate the final velocities of colliding spheres using the conservation of linear momentum, and has found a formula for this. They now want to know how to use the conservation of angular momentum to determine the angular velocities of spinning spheres after collision and how much spin and angular momentum is transferred between the spheres. They also mention a thread where a similar topic was discussed and resulted in a working program.
  • #1
protolocke
3
0
Hi, I'm helping my friend with a space combat game he is programming. What I'm trying to figure out is how to model the collisions between spheres in 3D.

So far I've figured out how to calculate final velocities of 2 colliding spheres using conservation of linear momentum. I found a http://www.wheatchex.com/projects/collisions/" which gives me this formula:

v1f = v1i - ((m2c)/(m1 + m2))(1 + e)n
v2f = v2i + ((m1c)/(m1 + m2))(1 + e)n

where

v1i = the initial velocity of object 1
v2i = the initial velocity of object 2
m1 = the mass of object 1
m2 = the mass of object 2
e = the coefficient of restitution (e = 1 for elastic collision)
n = normal unit vector drawn from object 1 to object 2
c = n . (v1i - v2i)

My question is, using conservation of angular momentum, how would I work out the angular velocities of spinning spheres after they collide? How much spin is transferred from one sphere to another? How much angular momentum, if any, would be converted to linear momentum?

Thanks for your time
 
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  • #2
Take a look at this thread, where we discuss something similar, that resulted eventually in a working program.
 

FAQ: 3D elastic collisions of spheres: angular momentum

1. What is a 3D elastic collision?

A 3D elastic collision is a type of collision that occurs between two or more objects in three-dimensional space where the total kinetic energy of the system is conserved. This means that the objects involved in the collision do not experience any loss of energy due to deformation or friction.

2. How is angular momentum conserved in 3D elastic collisions?

In a 3D elastic collision, the total angular momentum of the system is conserved. This means that the initial angular momentum of the objects before the collision is equal to the final angular momentum of the objects after the collision. This conservation is due to the fact that the forces involved in the collision act along the line of impact, resulting in no net torque on the system.

3. Can you explain the difference between elastic and inelastic collisions?

In an elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some of the kinetic energy is lost due to deformation or other factors. Inelastic collisions also typically involve objects sticking together after the collision, while in elastic collisions, the objects bounce off of each other.

4. How do you calculate the final velocities of objects after a 3D elastic collision?

The final velocities of objects after a 3D elastic collision can be calculated using the conservation of momentum and the conservation of kinetic energy equations. These equations take into account the masses and initial velocities of the objects involved in the collision, as well as the angle of impact and the coefficient of restitution, which represents the elasticity of the collision.

5. What are some real-life applications of 3D elastic collisions?

3D elastic collisions can be observed in many real-life situations, such as billiard balls colliding on a pool table, balls bouncing off of each other in a game of pinball, or particles colliding in a particle accelerator. Understanding the principles of 3D elastic collisions is also important in fields such as engineering, physics, and materials science.

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