Linear Momentum and Conservation

Overview

Momentum is a vector quantity, so direction matters. In one-dimensional problems, the key skill is choosing a sign convention and applying conservation of momentum to the system before and after the interaction.

What You Need to Know

• Linear momentum is p = mv.
• The total momentum of a system is conserved when no resultant external force acts on it.
• In one-dimensional collisions, choose one direction as positive and keep signs consistent.
• In an elastic collision, total kinetic energy is conserved.
• In an inelastic collision, momentum is still conserved but kinetic energy is not.

How to Work Through It

1. Start by calculating momentum for single moving objects, including direction.
2. Set up before-and-after tables for simple collisions and explosions.
3. Use conservation of momentum to find an unknown velocity or mass.
4. Check whether the interaction is elastic by comparing total kinetic energy before and after.

Check Your Understanding

• Why is momentum a vector?
• What must be true about external forces for system momentum to be conserved?
• How do you show an object moving in the negative direction in a calculation?
• What extra condition applies to an elastic collision?

Common Mistakes

• Adding speeds instead of signed velocities.
• Assuming kinetic energy is conserved in every collision.
• Forgetting that explosions also conserve momentum for the system.
• Mixing up momentum conservation with force balance.

Next Steps

• Practise using a before-and-after table for every momentum question.
• Keep sign conventions clear before moving into two-dimensional collisions.