What is Momentum?

Momentum

Momentum is a measure of how difficult it is to stop a moving object. It depends on both the mass and the velocity of the object.

Think about trying to stop a rolling shopping trolley versus a bicycle moving at the same speed. The heavier trolley is much harder to stop — that's because it has more momentum.

Momentum is calculated using the formula:

$p = m \times v$

Where:

$p$ = momentum (kg m/s)
$m$ = mass (kg)
$v$ = velocity (m/s)

Note

Momentum is a vector quantity — it has both magnitude (size) and direction. This means if two objects travel in opposite directions, their momenta can cancel or reduce each other.

The SI unit of momentum is kilogram metres per second (kg m/s).

Analogy

Imagine a slow-moving truck and a fast-moving tennis ball. The truck has huge mass but low speed; the tennis ball has tiny mass but high speed. Depending on the numbers, either could have more momentum — it's the combination of mass and velocity that matters.

Calculating Momentum

Let's practise applying the momentum formula $p = m \times v$ .

Example

Example 1: A moving car

A car of mass 1200 kg is travelling at 15 m/s. What is its momentum?

Step 1: Identify the values.

$m = 1200$ kg
$v = 15$ m/s

Step 2: Apply the formula.
$p = m \times v = 1200 \times 15 = 18, 000 kg m/s$

Answer: The car's momentum is 18,000 kg m/s in the direction of travel.

Example

Example 2: Rearranging for velocity

A football of mass 0.45 kg has momentum of 9 kg m/s. How fast is it moving?

Step 1: Rearrange the formula for $v$ .
$v = \frac{p}{m}$

Step 2: Substitute values.
$v = \frac{9}{0.45} = 20 m/s$

Answer: The football is moving at 20 m/s.

Exam Tip

Remember the formula triangle for momentum:

Cover $p$ → $m \times v$
Cover $m$ → $p \div v$
Cover $v$ → $p \div m$

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