Momentum

Momentum

how much motion you carry

Momentum is mass times velocity; a heavier or faster object carries more, and because velocity has a direction, so does momentum.

Example

Momentum is mass times velocity — a heavier or faster object carries more, and because velocity has a direction, so does momentum. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Momentum is mass times velocity

Momentum measures how much motion something carries: its mass times its velocity. A heavier cart or a faster cart has more. Because velocity has a direction, so does momentum.

p=m vp = m\,v
A moving cart carries momentumA cart on a track with a velocity arrow pointing in its direction of motion.mv

A worked value

A 2 kilogram cart rolling at 3 metres per second carries 2 times 3, or 6 kilogram metres per second of momentum, to the right. The same cart rolling the other way, left at 3 metres per second, would carry the opposite sign, minus 6 kilogram metres per second.

p=m v=2 kg ⋅ 3 m/s=6 kg m/sp = m\,v = 2\ \text{kg} \,\cdot\, 3\ \text{m}/\text{s} = \hl{6}\ \text{kg}\,\text{m}/\text{s}

Same speed, more mass, more momentum

Hold speed fixed. A heavier cart carries more momentum at the same velocity.

mvp1 kg3 m/s3 kg m/s2 kg3 m/s6 kg m/s3 kg3 m/s9 kg m/s\begin{array}{c|c|c}m & v & p \\ \hline 1\ \text{kg} & 3\ \text{m}/\text{s} & 3\ \text{kg}\,\text{m}/\text{s} \\ 2\ \text{kg} & 3\ \text{m}/\text{s} & 6\ \text{kg}\,\text{m}/\text{s} \\ 3\ \text{kg} & 3\ \text{m}/\text{s} & 9\ \text{kg}\,\text{m}/\text{s}\end{array}

Same mass, more speed, more momentum

Hold mass fixed. A faster cart carries more momentum, and the direction still follows the velocity.

mvp2 kg1 m/s2 kg m/s2 kg2 m/s4 kg m/s2 kg3 m/s6 kg m/s\begin{array}{c|c|c}m & v & p \\ \hline 2\ \text{kg} & 1\ \text{m}/\text{s} & 2\ \text{kg}\,\text{m}/\text{s} \\ 2\ \text{kg} & 2\ \text{m}/\text{s} & 4\ \text{kg}\,\text{m}/\text{s} \\ 2\ \text{kg} & 3\ \text{m}/\text{s} & 6\ \text{kg}\,\text{m}/\text{s}\end{array}
mechanics A 2 kg cart at 3 m/s gives a clean 6 kg m/s of momentum.