Introduction
Linear momentum is one of the most fundamental quantities in mechanics. It connects an object's mass with its velocity to give a single measure of its "quantity of motion." For the 9709 exam, you must be able to define momentum precisely, calculate it in one dimension, and demonstrate a clear understanding of its vector nature — meaning both magnitude and direction must be accounted for, and a sign convention must always be stated. Momentum also underpins the Impulse–Momentum principle and the Principle of Conservation of Momentum, which appear throughout the Mechanics unit.
Core Concept
What is Linear Momentum?
The linear momentum of a body is defined as the product of its mass and its velocity:
where:
- is the mass of the body (in kg), a positive scalar,
- is the velocity of the body (in m s), a vector quantity,
- is the momentum (in kg m s), a vector quantity.
Vector Nature of Momentum
Because velocity is a vector, momentum is also a vector. In one-dimensional motion, direction is captured entirely by the sign of the velocity. You must:
- Define a positive direction clearly at the start of every problem (e.g. "Taking motion to the right as positive").
- Assign positive or negative values to velocities accordingly.
- Carry the sign through all calculations — the sign of the momentum tells you its direction.
For example, if a ball of mass 0.5 kg moves to the left at 4 m s and rightward is positive, then:
The negative sign indicates the momentum is directed to the left.
Units
The SI unit of momentum is the kilogram metre per second, written as kg m s. This is equivalent to the newton-second (N s), which becomes relevant when linking momentum to impulse.
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