OCR A-level Mathematics A (H240) · 3.01 Quantities and Units in Mechanics
Mini-Lesson
Quantities and units
OCR section 3.01 is short, but every Mechanics mark depends on it: the SI units, the difference between a scalar and a vector, the difference between mass and weight, and the modelling assumptions that make the problems solvable.
We will use g = 9.8 m/s² in every calculation, and say so. Work through each screen, answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
Mechanics · units
SI units
Mechanics is built on three SI base units:
Mass — kilogram (kg)
Length — metre (m)
Time — second (s)
Everything else is derived from those:
Velocity / speed — m s−1
Acceleration — m s−2
Force / weight — newton (N). And since F = ma, 1 N = 1 kg m s−2.
Moment of a force — newton metre (N m)
Convert before you calculate. Mixing km/h with m/s, or grams with kilograms, wrecks the whole answer. To convert km/h to m/s, divide by 3.6; to go the other way, multiply by 3.6.
Calculate
Your turn — convert a speed
1Convert 72 km/h into m/s.
m/s
Hint: 72 km/h = 72 × 1000 m ÷ 3600 s = 72 ÷ 3.6.
Calculate
Your turn — convert back
2Convert 15 m/s into km/h.
km/h
Hint: multiply by 3.6: 15 × 3.6.
Mechanics · scalars and vectors
Scalars and vectors
A scalar has magnitude only. A vector has magnitude and direction.
distance & speed = SCALARS · displacement & velocity = VECTORSmass is a scalar · force, weight and acceleration are vectors
Why the distinction earns marks
Walk 5 m east, then 5 m west. The distance travelled is 10 m, but the displacement is 0 m — you are back where you started.
Over 10 s, the average speed is 10/10 = 1 m/s, but the average velocity is 0/10 = 0 m/s.
Signs carry the direction. In one-dimensional motion a vector is written as a signed number: choose a positive direction, then a velocity of −3 m/s simply means 3 m/s the other way. Declare your positive direction at the start — it is worth a mark.
Quick check
Scalar or vector?
?Which of these is a vector quantity?
Mechanics · weight
Mass, weight and g
Mass (kg) is how much matter an object contains — it never changes. Weight (N) is the force of gravity acting on that mass — and it is a vector, directed vertically downwards.
W = mg with g = 9.8 m s−2use g = 9.8 throughout this course unless a question tells you otherwise
Worked examples (taking g = 9.8 m/s²)
A mass of 6 kg has weight W = 6 × 9.8 = 58.8 N.
An object of weight 245 N has mass m = 245 ÷ 9.8 = 25 kg.
A 1200 kg car has weight 1200 × 9.8 = 11760 N = 11.76 kN.
The classic error: writing ‘the weight is 6 kg’. Kilograms measure mass; weight is a force and is measured in newtons. On the Moon that 6 kg mass is still 6 kg, but it weighs about a sixth as much.
Calculate
Your turn — weight from mass
3Find the weight of a mass of 6 kg. Take g = 9.8 m/s².
N
Hint: W = mg = 6 × 9.8.
Calculate
Your turn — mass from weight
4An object has a weight of 245 N. Find its mass. Take g = 9.8 m/s².
kg
Hint: m = W ÷ g = 245 ÷ 9.8.
Calculate
Your turn — a car's weight
5A car of mass 1200 kg rests on level ground. Find its weight in kilonewtons (kN), taking g = 9.8 m/s².
kN
Hint: W = 1200 × 9.8 = 11760 N. Then divide by 1000 to convert to kN.
Quick check
Mass or weight?
?Which statement is correct?
Mechanics · modelling
Modelling assumptions
Real objects are complicated. Mechanics questions simplify them with standard assumptions — and OCR expects you to know what each word means and what it lets you ignore.
Particle — the object is treated as a point; its size and shape are ignored, so it cannot rotate and there is no air resistance from its surface.
Light — the object’s mass is negligible. A light string means the tension is the same throughout it.
Inextensible — the string does not stretch, so two connected particles have the same speed and acceleration.
Smooth — there is no friction between the surfaces.
Rough — friction does act.
Rigid — the body does not bend; used for rods and beams in moments questions.
Smooth pulley — the tension is the same on both sides of the pulley.
Evaluate the model. A question may ask what effect an assumption has. “Modelling the ball as a particle ignores air resistance, so the real range would be less than calculated.” That kind of sentence is the mark.
Quick check
What does 'light' mean?
?In a mechanics question, a string is described as light. What does this tell you?
Quick check
The unit of acceleration
?What is the SI unit of acceleration?
Sort it
Scalar, vector or unit?
Tap a card, then tap the group it belongs to.
📏 Scalar
➡️ Vector
🔬 Unit
Match it
Modelling assumptions
Tap an assumption on the left, then what it actually means.
Assumption
Meaning
Recap
The big ideas to know
SI base units: kilogram (kg), metre (m), second (s)
Derived: velocity m s−1; acceleration m s−2; force newton, 1 N = 1 kg m s−2; moment N m
Scalars: distance, speed, mass — magnitude only
Vectors: displacement, velocity, acceleration, force, weight — magnitude and direction
Weight: W = mg, with g = 9.8 m/s²; measured in newtons, not kilograms
Converting: km/h → m/s: divide by 3.6
Assumptions: particle, light, inextensible, smooth, rigid — and be ready to evaluate them
That is OCR 3.01 — the vocabulary the rest of Mechanics is written in. Press Finish to see your score.
🏆
Mini-lesson complete!
⭐⭐⭐
You've worked through Quantities and units for OCR A-level Mathematics A. 🎉
Your stars: 0 / 0
Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.
📣 Smashed it? Share your score
Challenge a mate to beat your stars, or show a parent how you got on.