Momentum and Impulse

3.5 Momentum

Momentum (p) is the product of an object's mass (m) and velocity (v):

p = mv
  • Momentum is a vector quantity
  • SI unit: kilogram-meter per second (kg·m/s) or newton-second (N·s)

Example 3.4: Golf Ball Momentum

A 45g golf ball traveling at 80 m/s has a momentum of:

p = 0.045 kg × 80 m/s = 3.6 kg·m/s

3.5.1 Force and Change in Momentum

Newton's Second Law relates force and momentum:

F = ma = m(Δv / Δt) = Δp / Δt

The time rate of change of linear momentum equals the net force acting on the body.

Key Insight

For a sudden change in momentum, force is large. Increasing the duration of impact reduces the force.

3.5.2 Impulse and Change in Momentum

Impulse (J) is the product of force and time interval:

J = F × Δt = Δp
  • Impulse is a vector quantity
  • Direction is the same as the force causing it
  • SI units are the same as momentum

3.5.3 Conservation of Momentum

For an isolated system with no net external force:

ΔP = 0

Law of Conservation of Momentum:

"The momentum of an isolated system remains constant."

Application: Rocket Propulsion

Rockets accelerate in space by expelling hot gases with large momentum, gaining an equal and opposite momentum.