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: dp = Fdt, Δp = ∫Fdt, Δp = F_avgΔt.
The integral of force over time as Δt approaches 0 is called the impulse of the force.

Angular impulse: dL = τdt, ΔL = ∫τdt, ΔL = τ_avgΔt.
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.