AQA A-level Mathematics (7357) · Quantities and units in mechanics
Mini-Lesson
Quantities and units in mechanics
This mini-lesson covers AQA section P: the SI base quantities (length, time, mass) and the derived quantities you need in mechanics — velocity, acceleration, force, weight and moment — plus scalars vs vectors, converting units, and the relationship W = mg.
AQA section P: base quantities length, time, mass; derived quantities velocity, acceleration, force, weight, moment.
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Throughout this mini-lesson we use g = 9.8 m s⁻², the AQA convention, unless a question says otherwise. Press Start when you're ready.
Section P1 · SI system
Base and derived quantities
Mechanics is built from just three SI base quantities:
Length — metre (m)
Time — second (s)
Mass — kilogram (kg)
Everything else is derived by combining them:
Velocity = displacement ÷ time → m s⁻¹
Acceleration = change in velocity ÷ time → m s⁻²
Force = mass × acceleration → newton (N) = kg m s⁻²
Weight = mass × g → also measured in N (weight is a force)
Moment = force × perpendicular distance → N m
W = mg · g = 9.8 m s⁻²mass (kg) is how much matter there is · weight (N) is the force of gravity on it
g is not a universal constant. AQA is explicit: g depends on location (it is slightly smaller at the equator and up a mountain). We model it as constant at 9.8 m s⁻² near the Earth's surface. Some questions use 9.81 or 10 — always use the value you are given.
Calculate
Weight from mass
1A crate has mass 12 kg. Taking g = 9.8 m s⁻², calculate its weight.
N
Hint: W = mg = 12 × 9.8.
Calculate
Mass from weight
2An astronaut's toolbag weighs 49 N on Earth. Calculate its mass. (g = 9.8 m s⁻²)
kg
Hint: Rearrange W = mg → m = W ÷ g = 49 ÷ 9.8.
Quick check
Scalar or vector?
?Which of these is a scalar quantity?
Section P1 · conversions
Working with units
Marks are lost every year for mixing units. Convert before you substitute.
km h⁻¹ → m s⁻¹: multiply by 1000 and divide by 3600, i.e. ÷ 3.6.
tonnes → kg: × 1000. grams → kg: ÷ 1000.
cm → m: ÷ 100. minutes → s: × 60.
Worked example
Convert 72 km h⁻¹ into m s⁻¹.
72 km = 72 000 m; 1 hour = 3600 s.
72 000 ÷ 3600 = 20 m s⁻¹
Dimension check: N = kg m s⁻², so N m = kg m² s⁻² — the same combination as an energy in joules. That is why a moment is written as N m and never as "joules": the physical meaning is different.
Calculate
Unit conversion
3A car travels at 72 km h⁻¹. Convert this to m s⁻¹.
m s⁻¹
Hint: Divide by 3.6, or: 72 × 1000 ÷ 3600.
Calculate
Moment
4A force of 15 N acts at a perpendicular distance of 0.4 m from a pivot. Calculate the moment.
N m
Hint: Moment = force × perpendicular distance = 15 × 0.4.
Calculate
Newton's second law
5A car of mass 900 kg accelerates at 1.5 m s⁻². Calculate the resultant force on it.
N
Hint: F = ma = 900 × 1.5.
Sort it
Scalar, vector, or unit?
Tap a card, then tap the box it belongs in.
📏 Scalar
➡️ Vector
🔤 Unit
Quick check
The newton in base units
?The newton is a derived unit. Which combination of base units is equivalent to 1 N?
Match it
Unit → quantity
Tap a unit on the left, then the quantity it measures on the right.
Unit
Quantity
Quick check
Mass or weight?
?A student writes: "The mass of the box is 60 N." What is wrong?
Quick check
Name the quantity
?Which quantity is measured in N m?
Modelling · assumptions
The modelling words examiners use
Every mechanics question hides its assumptions in a few key words. Learn exactly what each one buys you:
Particle — the object's mass is at a single point; its size and any rotation are ignored (so you can ignore moments).
Light — the mass is negligible, so the object has no weight (a light string, a light rod).
Inextensible — a string does not stretch, so connected particles have the same magnitude of acceleration.
Rigid — the body does not bend, so a rod stays straight.
Small object thrown in the air, ignoring air resistance — so the only force is weight.
Exam skill: "State one assumption you have made and how it affects your answer." A good answer: "I ignored air resistance; in reality it would oppose the motion, so the true speed would be less than my value."
Vectors · components
Forces as vectors
A force in two dimensions can be written in component (i, j) form. To combine forces, just add the components.
|F| = √(x² + y²)the magnitude of F = xi + yj, in newtons
Worked example
A particle is acted on by F = (6i + 8j) N.
|F| = √(6² + 8²) = √(36 + 64) = √100 = 10 N
By F = ma, a 2 kg particle would accelerate at (3i + 4j) m s⁻², of magnitude 5 m s⁻².
Calculate
Magnitude of a force
6A force is F = (6i + 8j) N. Calculate its magnitude.
N
Hint: |F| = √(6² + 8²) = √(36 + 64).
Quick check
The particle model
?A question says: "A car of mass 900 kg is modelled as a particle." What does that assumption mean?
Recap
The big ideas to know
Base quantities: length (m) · time (s) · mass (kg)
Derived: velocity (m s⁻¹) · acceleration (m s⁻²) · force & weight (N) · moment (N m)
1 N = 1 kg m s⁻² — the force giving a 1 kg mass an acceleration of 1 m s⁻²
W = mg with g = 9.8 m s⁻² (AQA convention); g depends on location, so it is a model
Scalars: mass, speed, distance, time · Vectors: displacement, velocity, acceleration, force
Convert first: km h⁻¹ ÷ 3.6 → m s⁻¹ · tonnes × 1000 → kg
That is the whole of section P — Quantities and units in mechanics for AQA A-level Mathematics (7357). Press Finish to see your score.
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