Momentum

Momentum measures how hard it is to stop a moving object. A fast, heavy truck has more momentum than a slow, light bicycle. Momentum depends on both mass and velocity.

Key idea and equation

Momentum (symbol p) is defined as mass × velocity.

$$p = m v$$

Units: kilograms metre per second (kg m s⁻¹). Momentum has a direction. Choose one direction as positive; the opposite direction is negative.

Impulse and changing momentum

Impulse is the force multiplied by the time the force acts. It equals the change in momentum.

$$\text{impulse} = F\,\Delta t = \Delta (mv) = \Delta p$$

Spreading a change in momentum over a longer time reduces the force. This is why airbags and helmets increase stopping time to reduce force on the person.

Resultant force and momentum

The average resultant force relates to momentum change:

$$F_{\text{resultant}} = \dfrac{\Delta p}{\Delta t}$$

If mass is constant, this becomes $F = ma$.

Conservation of momentum (1D)

In a closed system with no external forces, total momentum stays the same during a collision or explosion.

$$\text{total } p_{\text{before}} = \text{total } p_{\text{after}}$$

Use signs for direction (e.g., right is positive, left is negative).

Common misconceptions

• “Momentum is the same as force.” Force changes momentum; they are not the same.
• “Only speed matters.” Mass and velocity both matter for momentum.
• “Direction does not matter.” Momentum is a vector; include signs.