Law of Conservation of Momentum
The conservation of momentum calculator helps you analyze the motion of two colliding objects. The principle of momentum conservation states that for an isolated system, the total momentum of all objects remains constant — whatever momentum is lost by one object is gained by the other.
What Is Momentum?
Momentum (p) is the product of an object's mass and velocity: p = m × v. It is a vector quantity, measured in kg·m/s (Newton-seconds) in the metric system or lb·ft/s in the US customary system.
The Law of Conservation of Momentum
In an isolated system (no external forces), the total momentum before a collision equals the total momentum after:
m₁·v₁ᵢ + m₂·v₂ᵢ = m₁·v₁f + m₂·v₂f
Types of Collisions
- Elastic collision — Both momentum and kinetic energy are conserved. Objects bounce off each other (e.g., billiard balls, marbles).
- Perfectly inelastic collision — Momentum is conserved but kinetic energy is not. Objects stick together and move with a common final velocity (e.g., a bullet embedding in a wooden block).
- Partially inelastic (custom) collision — Momentum is conserved; you know the final velocity of one object and the calculator finds the other. Some kinetic energy is lost to deformation or heat.
How to Use This Calculator
- Select your unit system: Metric (kg, m/s) or Imperial (lb, ft/s).
- Enter the mass and initial velocity of each object. Use a negative value if the object moves in the opposite direction. Set velocity to 0 for a stationary object.
- Choose the collision type:
- Elastic — calculator computes both final velocities automatically.
- Perfectly Inelastic — both objects stick together; one combined final velocity is calculated.
- Custom — enter the final velocity of Object 1; the calculator finds Object 2's final velocity.
- Click Calculate Momentum to see results including final velocities, momentum breakdown, kinetic energy analysis, and collision classification.
Example
Object 1: mass = 8 kg, initial velocity = 10 m/s. Object 2: mass = 4 kg, initially at rest (v = 0).
Initial total momentum: 8 × 10 + 4 × 0 = 80 kg·m/s
After an elastic collision: v₁f = 3.333 m/s, v₂f = 13.333 m/s. Final total momentum = 80 kg·m/s ✓
FAQs
Is momentum always conserved?
Momentum is conserved in an isolated system where the net external force is zero. In real-world scenarios, friction, gravity, or other external forces may cause momentum to change.
What is the difference between elastic and inelastic collisions?
In an elastic collision, both momentum and kinetic energy are conserved — objects bounce off without permanent deformation. In an inelastic collision, momentum is conserved but kinetic energy decreases (converted to heat, sound, or deformation). In a perfectly inelastic collision, the objects stick together.
Can momentum be negative?
Yes. Momentum is a vector quantity. If an object moves in the negative direction (opposite to the chosen positive direction), its velocity — and therefore momentum — is negative.
What units does this calculator use?
In metric mode: mass in kilograms (kg), velocity in meters per second (m/s), momentum in kg·m/s (= N·s), kinetic energy in Joules (J).
In imperial mode: mass in pounds (lb), velocity in feet per second (ft/s), momentum in lb·ft/s, kinetic energy in ft·lbf.