Key Equations

impulse

F_{net} Δ t

impulse–momentum theorem

Δ p = F_{net} Δ t

linear momentum

p = m v

Newton’s second law in terms of momentum

F_{net} = \frac{Δ p}{Δ t}

law of conservation of momentum

p_tot = constant, or p_tot = p′_tot

conservation of momentum for two objects

p₁ + p₂ = constant, or p₁ + p₂ = p′₁ + p′₂

angular momentum

L = I

ω

conservation of momentum in any collision, including elastic collisionselastic collision

m_{1} v_{1} + m_{2} v_{2} = m_{1} {v^{'}}_{1} + m_{2} {v^{'}}_{2},

conservation of momentum in a perfectly inelastic collision

m_{1} v_{1} + m_{2} v_{2} = (m_{1} + m_{2}) v^{'}

conservation of momentum along x-axis for 2D collisions

m_{1} v_{1} = m_{1} {v^{'}}_{1} \cos θ_{1} + m_{2} {v^{'}}_{2} \cos θ_{2}

conservation of momentum along y-axis for 2D collisions

0 = m_{1} v^{'}_{1} \sin θ_{1} + m_{2} v^{'}_{2} \sin θ_{2}