Table of Contents
What Are Impulse and Momentum?
Momentum is the product of an object's mass and velocity, representing the quantity of motion the object possesses. It is a vector quantity measured in kilogram-meters per second (kg-m/s) or equivalently Newton-seconds (N-s). An object with greater mass or greater velocity has greater momentum, and therefore requires a greater force to stop it.
Impulse is the change in momentum experienced by an object when a force acts on it over a period of time. It equals the product of the average force and the time duration over which the force is applied. The impulse-momentum theorem states that the impulse delivered to an object equals the change in its momentum, forming one of the most powerful principles in classical mechanics.
The Impulse-Momentum Theorem
Where J is impulse, Δp is the change in momentum, m is mass, vf and vi are final and initial velocities, Favg is the average force, and Δt is the time interval.
Real-World Examples
| Scenario | Contact Time | Why It Matters |
|---|---|---|
| Airbag deployment | ~0.1 s | Extends impact time, reducing peak force on occupant |
| Baseball bat hitting ball | ~0.001 s | Short time = very high average force (~8,000 N) |
| Catching a ball with hands | ~0.05 s | Moving hands back extends time, reduces force |
| Rocket thrust | Continuous | Sustained force produces continuous momentum change |
Conservation of Momentum
- In an isolated system (no external forces), total momentum is always conserved.
- This principle governs collisions, explosions, rocket propulsion, and recoil.
- In elastic collisions, both momentum and kinetic energy are conserved.
- In inelastic collisions, momentum is conserved but kinetic energy is not.
Frequently Asked Questions
Why do airbags reduce injury?
Airbags increase the collision time from a few milliseconds (hitting a hard steering wheel) to about 100 milliseconds. Since impulse (change in momentum) is the same regardless of collision time, a longer time means a smaller average force: F = Δp/Δt. Reducing peak force by a factor of 10 or more can be the difference between a survivable and fatal crash.
Can impulse be negative?
Yes. Impulse is a vector quantity. A negative impulse means the force acts in the negative direction, decreasing the object's momentum. For example, when you apply brakes to a car, the friction force creates a negative impulse that reduces the car's forward momentum.
What units is impulse measured in?
Impulse is measured in Newton-seconds (N-s) or equivalently kilogram-meters per second (kg-m/s). These are the same units as momentum, which makes sense because impulse equals the change in momentum. In the imperial system, impulse is measured in pound-force-seconds (lbf-s).