• The vector p has the same direction as the velocity of the body
• When the net external force on a system is zero, the system is isolated and results in the momentum p staying constant over time (i.e. p_initial = p_final when F_net = 0)
• Change in momentum: Δp = p_final - p_initial
• Net force is the change in momentum over time: F_net = Δp/Δt

• J = Ft, where J is the impulse (kg⋅m⋅s^-1), F is the average net force (N), and t is how long the force acts on the system (s)
• Hence, if you want the momentum of an object to change a lot, then you must either apply a large amount of force, or apply a force for a long time
• The area under a line/curve of a force vs time graph represents the impulse

Momentum in Collisions

• If the system is isolated, the total momentum is conserved, and p_initial = p_final
• Hence, for a collision between two balls where the system is isolated, the total momentum before the collision is equal to the total momentum after the collision: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Energy in Collisions

• In an elastic collision, the total kinetic energy of the system is conserved, hence the total kinetic energy before the collision is equal to the total kinetic energy after
• In an inelastic collision, the total kinetic energy after the collision is less than the total kinetic energy before the collision (kinetic energy is lost), hence the total kinetic energy of the system is not conserved

• An explosion can be studied as an inelastic collision happening backwards
• The total momentum before and after a collision is zero
• However, the total kinetic energy of the system is not conserved during an explosion, because the total kinetic energy after the collision is greater than before the collision - thus kinetic energy is gained