Momentum Calculations

Momentum is the product of an object’s mass and its velocity. It is a vector quantity: it has both size and direction.

The equation

$p = mv$

Symbol	Quantity	Unit
$p$	Momentum	kg m/s
$m$	Mass	kg
$v$	Velocity	m/s

Direction matters

Because velocity is a vector, momentum has a direction. When solving problems with objects moving in opposite directions, assign one direction as positive and the other as negative.

Worked example

A car of mass 1500 kg travels at 20 m/s to the right. Calculate its momentum.

$p = 1500 \times 20 = 30\,000\text{ kg m/s to the right}$

Worked example: direction

A 0.50 kg ball moves to the right at 8.0 m/s. After bouncing off a wall it moves to the left at 6.0 m/s. Taking right as positive:

Before: $p = 0.50 \times (+8.0) = +4.0$ kg m/s

After: $p = 0.50 \times (-6.0) = -3.0$ kg m/s

Change in momentum = $-3.0 - (+4.0) = -7.0$ kg m/s (to the left).

Common errors and how to correct them

Forgetting to include direction. Momentum is a vector. Always state the direction alongside the numerical value.

Using speed instead of velocity in problems where direction changes. When an object bounces or reverses, the velocities before and after have opposite signs.

How to apply this in an exam

State the equation, show substitution, include the unit (kg m/s) and the direction. When calculating change in momentum, use $\Delta p = mv - mu$ with correct signs.