Conservation of Momentum Calculator

The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act upon it. In a collision between two objects, the total momentum before the collision equals the total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.

In a perfectly elastic collision, both momentum and kinetic energy are conserved — the objects bounce off each other with no energy loss. In a perfectly inelastic collision, the objects stick together after impact, momentum is still conserved, but kinetic energy is not — some energy is converted to heat, sound, or deformation.

Momentum is conserved in any isolated system where no net external forces act on the objects. In practice, this means collisions that happen quickly enough that external forces (like friction or gravity) have negligible effect during the collision interval. Both elastic and inelastic collisions conserve total momentum.

A classic example is billiard balls: when the cue ball strikes a stationary ball, momentum transfers from the cue ball to the target ball. Another example is a rocket — it ejects exhaust gases backward at high speed, and by conservation of momentum the rocket moves forward. Newton's cradle also demonstrates this principle visually.

For a perfectly elastic collision, two equations are used simultaneously: conservation of momentum (m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂) and conservation of kinetic energy. Solving these gives: v₁ = ((m₁ − m₂)u₁ + 2m₂u₂) / (m₁ + m₂) and v₂ = ((m₂ − m₁)u₂ + 2m₁u₁) / (m₁ + m₂).

When two objects collide and stick together, they move as one combined mass. The final velocity is calculated using: vf = (m₁u₁ + m₂u₂) / (m₁ + m₂). This applies conservation of momentum, and the single resulting velocity is shared by both objects.

Yes. Negative velocity values represent motion in the opposite direction. For example, if Object 1 moves to the right at +10 m/s and Object 2 moves to the left at −5 m/s, you would enter 10 and −5 respectively. The calculator handles direction correctly using signed values.

This calculator assumes a closed, isolated 1D system with no external forces. It does not account for friction, air resistance, rotational effects, or 2D/3D collisions. Real-world collisions may only be approximately elastic or inelastic, so results are idealized. For partially elastic collisions, a coefficient of restitution approach would be needed.