Introduction
Conservation of linear momentum is one of the most powerful principles in mechanics. It allows us to find unknown velocities after a collision without needing to know anything about the forces acting during the impact — only the masses and velocities before and after matter. In the 9709 exam, questions on this topic typically ask you to find a velocity after a direct collision, determine a mass, or decide the direction of motion of a body after impact. Coalescence (where two bodies stick together and move as one) is a particularly common scenario worth mastering.
Core Concept
The Principle of Conservation of Linear Momentum states:
When no external force acts on a system of bodies along a given line, the total linear momentum of the system is constant.
In a direct impact (head-on collision along a straight line), the two bodies exert equal and opposite forces on each other (Newton's Third Law) for the same duration. These internal forces cancel out, so the total momentum is conserved.
Momentum is a vector quantity — direction matters. We always set a positive direction at the start and treat velocities in the opposite direction as negative.
For two bodies colliding directly:
where are masses and , are velocities before and after the collision respectively.
Coalescence: If the two bodies stick together on impact, they move with a single common velocity after the collision:
The number of unknowns reduces to one, making these the most straightforward collision problems.
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