Carry units through every line of a calculation. If the units on the right do not match the quantity you want, something is wrong before you even finish.
This lesson is part of the SPM subjects and learning resources section. The examples are original and conceptual; check the formulas expected in your syllabus with your teacher.
How do I check units?
- Convert every quantity to the base unit first (m, kg, s, N).
- Write the unit beside each number in the substitution line.
- Multiply or divide the units as well as the numbers.
- Check that the final unit is the one the question asks for.
Worked example: moment of a force
This is a worked example. A force of 25 N acts on a door handle 60 cm from the hinge, perpendicular to the door. Find the moment about the hinge.
Step 1: convert. 60 cm = 0.60 m.
Step 2: substitute with units. Moment = F × d = 25 N × 0.60 m.
Step 3: calculate. 25 × 0.60 = 15, and N × m = N m.
Answer: 15 N m.
Worked example: pressure
A block presses on a table with a force of 50 N. The area in contact is 0.02 m². Pressure = force ÷ area = 50 N ÷ 0.02 m² = 2 500 N/m², which is 2 500 Pa.
Units check: N ÷ m² gives N/m², and 1 N/m² is 1 Pa, so the unit matches pressure.
The mistake that costs marks
The common slip is to multiply 25 N by 60 without converting, which gives 1 500 and a wrong answer by a factor of 100. The result may even be labelled “N m”, which hides the error.
| Step | Slip | Correct |
|---|---|---|
| Distance | 60 cm used directly | 0.60 m |
| Calculation | 25 × 60 = 1 500 | 25 × 0.60 = 15 |
| Answer | 1 500 N m | 15 N m |
Check the size of the answer too
Ask whether the answer is reasonable. A 25 N push on a 0.6 m handle giving 1 500 N m would be as large as a heavy machine’s turning effect, which is not plausible for a door.
Check yourself
A force of 120 N acts on a wrench at a distance of 35 cm from the bolt, perpendicular to the handle. Find the moment in N m. Then find the work done in joules when a 120 N force moves a crate 3 m in the direction of the force.
Answer
Moment: 35 cm = 0.35 m. Moment = 120 N × 0.35 m = 42 N m.
Work: W = F × d = 120 N × 3 m = 360 J.
Both use newtons times metres, but the moment is a turning effect and the work is energy transferred. Name the quantity in your answer so the unit makes sense.
What to study next
Practise linking a real observation to a model in link an observation to a mechanical model. Then try the Mechanical Engineering original practice set.
The structured answer self-review reminds you to check units and size. A teacher can go through your own calculations in online one-to-one Mechanical Engineering tuition.