Conservation of Momentum Calculator

How it works

1. 1Enter the mass and initial velocity of each object. Toggle between metric (kg, m/s) and imperial (lb, ft/s).
2. 2The calculator converts inputs to SI, then finds the conserved system momentum m₁u₁ + m₂u₂.
3. 3It also computes the common final velocity if the objects stick together: (m₁u₁ + m₂u₂) ÷ (m₁ + m₂).

Use cases

• Physics homework — verifying momentum conservation in collision problems.
• Engineering — estimating post-impact velocities for crash analysis or buffer design.
• Sports science — analysing player or ball collisions and momentum transfer.

Frequently asked questions

What is the law of conservation of momentum?

The total linear momentum of a closed system stays constant when no net external force acts. For two objects: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where u is initial and v is final velocity.

What formula does this calculator use?

Total momentum p = m₁u₁ + m₂u₂ (kg·m/s). For a perfectly inelastic collision: v = (m₁u₁ + m₂u₂) ÷ (m₁ + m₂). Momentum is always conserved; kinetic energy is not in an inelastic collision.

Worked example — two carts that collide and stick?

Cart 1: 2 kg at 5 m/s. Cart 2: 3 kg at 1 m/s. Total = (2 × 5) + (3 × 1) = 13 kg·m/s. Common velocity = 13 ÷ 5 = 2.6 m/s. Total momentum is 13 kg·m/s both before and after.