Definitions

• Momentum (p) is the product of an object's mass and velocity:
• p = mv
• It is a vector quantity measured in kg·m/s

Derivation from Newton's Second Law

Starting with F = ma and noting that a = Δv/Δt:

• F = m(Δv/Δt) = Δ(mv)/Δt = Δp/Δt

Therefore, force equals the rate of change of momentum.

Internal vs External Forces

• Internal Forces: Forces between objects within a system (cancel out by Newton's 3rd law)
• External Forces: Forces from outside the system that can change the system's total momentum

Conservation of Momentum

In the absence of external forces, the total momentum of a system remains constant:

• pinitial = pfinal
• (m₁v₁)ᵢ + (m₂v₂)ᵢ = (m₁v₁)f + (m₂v₂)f

This principle is fundamental in analyzing collisions and explosions.

Impulse

Impulse is the change in momentum, equal to force multiplied by time:

• J = FΔt = Δp

Variables: