Forces and motion units
Mechanics units connect each quantity to a measurable physical meaning, from base units for motion to compound units for force, field strength and momentum.
- Syllabus
- 2024
- Topic
- —
- Level
- —
Learning objectives
Choose the correct unit in mechanics
A number in mechanics is complete only when its unit identifies the physical quantity. The unit symbol is case-sensitive: m is metre, while N is newton.
| Quantity | Unit | Symbol | What the form tells you |
|---|---|---|---|
| mass | kilogram | kg | amount of mass |
| length or distance | metre | m | position or distance travelled |
| time | second | s | duration |
| speed or velocity | metre per second | m/s | metres travelled each second |
| acceleration | metre per second squared | m/s² | change in velocity each second |
| force | newton | N | size of a force |
| gravitational field strength | newton per kilogram | N/kg | force on each kilogram of mass |
m/s and m/s2 describe different quantities: acceleration has an extra “per second” because velocity itself changes with time. N/kg is used for gravitational field strength, not as another way to label every acceleration.
Build units for moments and momentum
A compound unit follows the quantities in the relationship. Multiplication places unit symbols side by side; division keeps the divisor below the line or after a slash.
| Quantity | How its unit is built | Required unit |
|---|---|---|
| moment of a force | force × perpendicular distance | newton metre, Nm |
| momentum | mass × velocity | kilogram metre per second, kgm/s |
For momentum, multiplying kg by m/s gives kgm/s. For a moment, multiplying N by m gives Nm. These unit structures provide a quick check that the chosen relationship uses the correct quantities.
Nm means newton multiplied by metre, not N/m. Momentum uses kgm/s; kgm/s2 instead has the same base-unit structure as a newton and is not the unit of momentum.