Momentum

• Momentum = mass × velocity; it is a vector, so in one dimension its sign shows the direction.
• Conservation of linear momentum: total momentum before a direct impact = total momentum after.
• If the bodies coalesce, they move off together with one common velocity.
• Impulse and the coefficient of restitution are NOT on this syllabus — the second equation always comes from the question.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Momentum is mv, measured in N s (or kg m s⁻¹). Because it is a vector, choose a positive direction and give every velocity a sign: a particle moving the other way has a negative velocity. Draw a "before" and "after" diagram with all unknown velocities drawn in the positive direction; a negative answer then simply means the particle moves the other way.

In a direct impact the internal forces cancel, so total momentum is conserved. If the particles coalesce (stick together), the "after" is a single particle of mass m₁ + m₂. Kinetic energy is usually lost — you may be asked for the loss, using ½mv².