CCEA GCE Mathematics (2210) · Quantities and units in mechanics
Mini-Lesson
Quantities and units in mechanics
Mechanics starts with getting the quantities right. This mini-lesson covers SI base and derived units, the difference between scalars and vectors, mass vs weight, unit conversion, and the modelling assumptions (particle, light, inextensible, smooth, rigid) that every mechanics question quietly relies on. Throughout we use g = 9.8 m s⁻².
Where this sits:Unit AS 2: Applied Mathematics — quantities and units in mechanics: use of SI units, and the modelling assumptions that underpin mechanical models.
Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Press Start when you are ready.
SI units
Base and derived units
Mechanics uses the SI system. Three base units carry almost everything:
length — metre (m) · mass — kilogram (kg) · time — second (s)
Everything else is derived:
1 N = 1 kg m s⁻²from F = ma: the force that gives 1 kg an acceleration of 1 m s⁻²
velocity: m s⁻¹ · acceleration: m s⁻² · force and weight: N · momentum: kg m s⁻¹ · impulse: N s
Always convert first. Mixing km/h with m/s, or grams with kilograms, wrecks an otherwise perfect solution. To convert km/h → m/s, divide by 3.6.
Calculate
Weight from mass
1Take g = 9.8 m s⁻². Find the weight of a 5 kg mass.
N
Hint: Weight W = mg = 5 × 9.8. Weight is a FORCE, measured in newtons.
Calculate
Convert speed
2Convert 72 km/h into metres per second.
m/s
Hint: 72 km/h = 72000 m ÷ 3600 s = 72 ÷ 3.6.
Mass and weight
They are not the same
W = mgmass (kg) is a SCALAR and never changes · weight (N) is a VECTOR force, always vertically downwards
Take a 5 kg bag to the Moon: its mass is still 5 kg, but its weight falls from 49 N to about 8 N because g is smaller there.
Worked example — mass from weight
An object weighs 78.4 N on Earth. Find its mass.
m = W/g = 78.4 ÷ 9.8 = 8 kg
Language: "a mass of 5 kg" is correct; "a weight of 5 kg" is not. Kilograms measure mass; newtons measure weight.
Calculate
Mass from weight
3An object has weight 78.4 N. Taking g = 9.8 m s⁻², find its mass.
kg
Hint: m = W ÷ g = 78.4 ÷ 9.8.
Scalars and vectors
Two kinds of quantity
Scalar — magnitude only: mass, speed, distance, time, energy.
Vector — magnitude and direction: displacement, velocity, acceleration, force, momentum.
Why it matters: a ball thrown up and caught again has travelled a distance of (say) 10 m but has a displacement of 0. Similarly its average speed is non-zero while its average velocity is zero. Vectors also mean you must fix a positive direction and stick to it, giving quantities in the other direction a minus sign.
Calculate
F = ma
4A resultant force of 12 N acts on a particle of mass 0.4 kg. Find its acceleration.
m/s²
Hint: a = F ÷ m = 12 ÷ 0.4.
Calculate
Force needed
5A 2000 kg lorry accelerates at 1.5 m s⁻². Find the resultant force on it.
N
Hint: F = ma = 2000 × 1.5.
Modelling
The assumptions behind every question
Mechanics questions simplify reality. You must know what each phrase means and what it lets you ignore:
Particle — the body has mass but no size, so rotation and air resistance on its shape are ignored, and all forces act at one point.
Light (string, rod, pulley) — its mass is negligible, so it has no weight and the tension is unchanged along it.
Inextensible string — it does not stretch, so connected particles have the same speed and acceleration.
Smooth — no friction acts.
Rough — friction acts, up to F ≤ μR.
Rigid rod / rigid body — it does not bend; it can support moments.
Smooth pulley — the tension is the same on both sides of the string.
Evaluation marks: be ready to say how a model would change if an assumption were dropped — e.g. modelling air resistance would reduce the range of a projectile.
Quick check
Units of force
?The newton, expressed in SI base units, is:
Sort it
Scalar, vector or assumption?
Tap an item, then tap what it is.
📏 Scalar
➡️ Vector
🧠 Modelling assumption
Quick check
Mass on the Moon
?A 5 kg bag is taken to the Moon, where g ≈ 1.6 m s⁻². What happens?
Quick check
Why 'smooth'?
?A question says the plane is smooth. What does that let you do?
Match it
Match the unit or term
Tap the term on the left, then its meaning on the right.
Statement
Answer
Quick check
Distance or displacement?
?A runner completes one lap of a 400 m track, finishing where she started. What are her distance and displacement?
Examiner traps
Units and modelling pitfalls
Mass in kg, weight in N. "A weight of 5 kg" is wrong.
Convert before substituting: km/h ÷ 3.6 = m/s; g ÷ 1000 = kg.
State g = 9.8 m s⁻² and keep it consistent throughout the paper.
Fix a positive direction and give opposite-direction quantities a minus sign.
Know what each assumption buys you: smooth (no friction), light (no weight), inextensible (same acceleration), particle (no size or rotation).
Recap
The big ideas to know
SI base: m, kg, s · derived: 1 N = 1 kg m s⁻²
W = mg with g = 9.8 m s⁻² — mass (kg, scalar) is not weight (N, vector)
Scalar = size only · Vector = size + direction (choose a positive direction and stick to it)
Convert first: km/h ÷ 3.6 = m/s; grams ÷ 1000 = kg