## Impulsive forces

Forces and torques that act so powerfully but so briefly that they produce
finite changes in linear and angular momentum while the system undergoes
negligible displacement are said to be impulsive.

Linear impulse: d**p **=** F**dt, Δ**p
**=** **∫**F**dt, Δ**p
**=** F**_{avg}Δt.

The integral of force over time as Δt approaches 0 is called the
**impulse**
of the force.

Angular impulse: d**L **=** τ**dt, Δ**L
**=** **∫**τ**dt, Δ**L
**=** τ**_{avg}Δt.

The integral of torque over time as Δt approaches 0 is called the
**angular impulse** of the torque.

### Collisions

In collisions, it is assumed that the colliding particles interact for such a
short time, that the impulse due to external forces is negligible. Thus the
total momentum of the system just before the collision is the same as the total
momentum just after the collision.

- Elastic collision: momentum is conserved, mechanical energy is
conserved.
- Inelastic collisions: momentum is conserved, mechanical energy is not
conserved.

### Interacting objects

If no external forces act on a system of interacting objects, the center of
mass of the system does not accelerate. Any two interacting objects obey
Newton's third law.