The principle of conservation of momentum states that the total momentum in a system is the same before and after a collision, in the absence of other forces, i.e. in a closed system.

→ This leads to the derivation of the third relationship below.

The following relationship links, momentum, velocity and mass and can be used to solve problems involving these quantities of objects interacting in one dimension.

$$ \rho=mv $$

The total momentum present in a system is equal to the sum of the momentum of each individual object.

$$ \rho_{total}=\rho_a+\rho_b+... $$

$$ m_1u_1+m_2u_2=m_1v_1+m_2v_2 $$

The SI units of momentum are $kg \space ms^{-1}$.

There are different types of collisions, inelastic collisions, elastic collisions and explosions (a special type of collision that is a perfectly inelastic collision). What type of collision an interaction is relates to the kinetic energy present in the system before and after the collision.

In an inelastic collision, the momentum of the system is conserved, but the kinetic energy is not. There will be a greater total kinetic energy present in the system before the collision.

The other case is an explosion. An explosion is a special type of inelastic collision, where the momentum of the system is conserved by the kinetic energy is not — specifically, the total kinetic energy in the system after the collision will be greater than the total kinetic energy in the system before the collision.

In an elastic collision, both the momentum and the kinetic energy of the system is conserved. The total kinetic energy present in the system before and after the collision will be the same.

The formula relating kinetic energy, mass, and velocity can be used to solve problems involving the total kinetic energy of systems of interacting objects.

$$ E_k=\dfrac{1}{2}mv^2 $$

Newton’s third law states that every action force has an equal and opposite reaction force, this relates to action-reaction Newton force pairs and can be used to explain the forces in collisions.

When one object hits another in a collision, exerting a force, the second object exerts a force back on the first one that is equal and opposite.

The average force applied to an object, the time it is applied for, and impulse of the object are all linked by the following formula.