Base quantities and derived quantities

The S.I. system builds everything in mechanics from three 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 (and weight) → the newton, N. From F = ma, 1 N = 1 kg m s⁻²: the force that gives a 1 kg mass an acceleration of 1 m s⁻².
• Moment = force × perpendicular distance → N m

Mass is not weight. Mass is a scalar measured in kg — it never changes. Weight is the force of gravity on that mass, a vector measured in newtons: W = mg. Take g = 9.8 m s⁻² throughout. On the Moon g is smaller, so your weight falls but your mass does not.

Base or derived?

Weight from mass

Mass from weight

Scalar, vector, or a unit?

Tap an item, then tap the box it belongs in.

Scalars and vectors

A scalar has size only. A vector has size and direction. In mechanics the difference decides the sign of your answer.

• Scalars: distance, speed, mass, time, energy. Distance and speed are always positive.
• Vectors: displacement, velocity, acceleration, force, weight. These can be negative, meaning "in the negative direction".

Modelling words: a particle has no size (so all forces act at one point); a rod is light if its mass can be ignored; a string is inextensible if it does not stretch; a surface is smooth if there is no friction.

Spot the vector

Converting units

The exam expects you to convert into S.I. units before you calculate — most often km h⁻¹ → m s⁻¹.

Always convert first. Substituting km h⁻¹ into a formula that uses metres and seconds (like v = u + at with t in seconds) gives a badly wrong answer — and no marks.

km h⁻¹ → m s⁻¹

Force, weight and moment in action

The three derived quantities that dominate the mechanics papers:

Dimension check: if your answer has the wrong units, the working is wrong. A force must come out in N (kg m s⁻²); an acceleration in m s⁻². Checking units catches most slips.

Newton's second law

A moment

Unit or formula → quantity

Tap an item on the left, then its partner on the right.

The newton in base units

Mass vs weight

Modelling assumptions — and what they buy you

Every mechanics question is a model. The words in the question are instructions telling you what you are allowed to ignore.

• Particle — the object has no size, so its whole mass is at one point and it cannot rotate. You can ignore its dimensions.
• Light (string, rod, pulley) — its mass is negligible, so its weight is ignored and the tension is unchanged along it.
• Inextensible string — it does not stretch, so connected particles share the same speed and acceleration.
• Smooth — there is no friction (so F = 0, and a smooth pulley gives equal tension on both sides). Rough means friction acts.
• Rigid body / uniform rod — it does not bend, and a uniform rod's weight acts at its midpoint.
• g is constant at 9.8 m s⁻² — true near the Earth's surface, but g in fact varies slightly with location.

Exam question: "State one limitation of the model." Good answers: air resistance has been ignored; the object is not really a particle so it may spin; the string may stretch slightly; g is not exactly constant.

What the words mean

The big ideas to know

That is the whole of 9MA0 Topic 6 — Quantities and units in mechanics. Press Finish to see your score.