Conservation of Momentum
Total momentum is conserved without external forces.
Formula
Variables
Example
Basis of collision analysis
How it works
Momentum is a vector quantity equal to mass times velocity, so the total momentum of a system depends on both how much mass is moving and in what direction. If no net external force acts on the system, the internal forces between the objects are equal and opposite, so they can change each object’s momentum but cannot change the system’s total momentum. That is why the total momentum before an interaction must equal the total momentum after it.
When to use it
Use this for systems where objects interact briefly and external forces are negligible, such as carts colliding, people jumping off boats, or explosions. It is especially useful when you need to relate unknown final speeds or directions after an interaction.
Worked example, step by step
A 0.50 kg cart moving right at 4.0 m/s collides and sticks to a 1.50 kg cart initially at rest. Step 1: Write the conservation equation: total initial momentum = total final momentum. Step 2: Initial momentum = (0.50 kg)(4.0 m/s) + (1.50 kg)(0 m/s) = 2.0 kg·m/s. Step 3: After sticking together, total mass = 0.50 kg + 1.50 kg = 2.00 kg. Step 4: Let the shared final velocity be v. Final momentum = (2.00 kg)v. Step 5: Set initial and final momentum equal: 2.0 = 2.00v. Step 6: Solve: v = 1.0 m/s. Final answer: the two carts move together at 1.0 m/s to the right.
Common mistakes to avoid
- Forgetting momentum is a vector and mixing up left/right or positive/negative directions
- Using conservation of momentum when a significant external force, like friction, acts on the system
- Conserving kinetic energy instead of momentum in an inelastic collision
Did You Know?
Total momentum is conserved in every collision, which is how physicists reconstruct car crashes and particle smashups.
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More in Physics Laws & Theorems
View allNewton's First Law (Inertia)
BasicAn object stays at rest or in uniform motion unless acted on by a net force.
Newton's Second Law
BasicNet force equals mass times acceleration (rate of change of momentum).
Newton's Third Law
BasicFor every action there is an equal and opposite reaction.
Conservation of Momentum
IntermediateTotal momentum of an isolated system stays constant.
Conservation of Energy
BasicEnergy cannot be created or destroyed, only transformed.
Archimedes' Principle
IntermediateBuoyant force equals the weight of fluid displaced.