A collision is an isolated event in which two or more bodies (colliding bodies) exert relatively strong forces on each other for a relatively short time.

Dynamics

The magnitude of the velocity difference at impact is called the closing speed.

The field of dynamics is concerned with moving and colliding objects.

Billiards

In billiards, collisions play an important role. Because the collisions between billiard balls are nearly elastic, and the balls roll on a surface that produces low-rolling friction, their behavior is often used to illustrate Newton's laws of motion. After a low-friction collision of a moving ball with a stationary one of equal mass, the angle between the directions of the two balls is 90 degrees. This appears to be an important fact that many professional billiard players take into account.

Consider an elastic collision in 2 dimensions of any 2 masses m₁ and m₂, with respective initial velocities v₁ in the x-direction, and v₂ = 0, and final velocities V₁ and V₂.

Conservation of momentum: m₁v₁ = m_1V1+m_2V2.

Conservation of energy for elastic collision: 1/2m₁|v₁|² = 1/2m₁|V₁|²+1/2m₂|V₂|²

Now consider the case m₁ = m₂, we then obtain v₁=V₁+V₂ and |v₁|² = |V₁|²+|V₂|²

Using the dot product, |v₁|² = v₁•v₁ = |V₁|²+|V₂|²+2V₁•V₂

So V₁•V₂ = 0, so they are perpendicular.

Traffic

In traffic such a collision can be between two vehicles, a vehicle and a person, a vehicle and an object, two persons or a person and an object (and more if an animal is involved). It is an accident or even a disaster. At level crossings sometimes a train collides with a vehicle or person. Due to the velocity and mass of a train it needs a long distance to stop, typically longer than the train driver can see ahead. When a train collides with a car this is more likely to be deadly for the people in the car than for those in the train, because the train has more mass and momentum.