Measuring length, volume & time

Physics rests on careful measurement. Cambridge expects you to choose the right instrument and to improve precision by measuring multiples:

• Length — a ruler (mm scale); read at eye level to avoid parallax error.
• Volume — a measuring cylinder for liquids; for an irregular solid that sinks, use displacement of water.
• Time — a clock or digital timer. For a short interval, time many repeats and divide. For a pendulum, time 10 swings and divide by 10 to get one period.

Why multiples? A single stopwatch reading carries your reaction-time error. Timing 10 oscillations and dividing by 10 shrinks that error tenfold.

Scalars vs vectors SUPP

A scalar has magnitude (size) only. A vector has magnitude and direction.

• Scalars: distance, speed, time, mass, energy, temperature.
• Vectors: force, weight, velocity, acceleration, momentum, electric & gravitational field strength.

Two vectors at right angles combine into a resultant found by Pythagoras (its size) and a direction:

Scalar or vector?

Speed, velocity & acceleration

Speed is the distance travelled per unit time. Velocity is speed in a stated direction (a vector).

An object near Earth's surface accelerates downward under gravity at g ≈ 9.8 m/s² — the acceleration of free fall. A deceleration is simply a negative acceleration.

Your turn — average speed

Reading a speed–time graph

On a speed–time graph two features carry all the information:

• The gradient (slope) = the acceleration.
• The area under the line = the distance travelled.

Watch out: a horizontal line on a speed–time graph means constant speed (zero acceleration), not "stopped". On a distance–time graph a horizontal line does mean at rest.

Your turn — acceleration from a graph

Mass is not weight

Mass is the quantity of matter in an object — measured in kg, the same everywhere. Weight is the gravitational force on that mass — measured in newtons (N).

Gravitational field strength g = W ÷ m. On Earth g ≈ 9.8 N/kg, and this number is equal to the acceleration of free fall (9.8 m/s²).

Watch out — the classic trap: your mass on the Moon is unchanged, but your weight is smaller because the Moon's g is only ~1.6 N/kg. Mass uses kg; weight uses N.

Your turn — weight

Density & the float/sink rule

Density is mass per unit volume — how tightly matter is packed:

To measure density: find mass on a balance; find volume with a measuring cylinder (liquid), ruler (regular solid) or displacement (irregular solid). Then ρ = m ÷ V.

Your turn — density

Hooke's law & spring constant

A force can change an object's size and shape. For a spring, the extension is proportional to the load — up to the limit of proportionality:

Watch out: x is the extension (the increase in length), not the spring's total length. Past the limit of proportionality the graph curves and Hooke's law no longer holds.

Your turn — spring constant

Resultant force & F = ma

Add forces along a straight line to find the resultant. The resultant decides the motion:

• Zero resultant → the object stays at rest or keeps moving in a straight line at constant speed.
• Non-zero resultant → the velocity changes (speed and/or direction).

Friction (drag) is the force between surfaces, or on an object moving through a liquid or gas (air resistance). It opposes motion and produces heating.

Watch out: balanced forces do not mean "stopped". A car at a steady 30 m/s has zero resultant force — constant velocity. Force causes acceleration, not velocity itself.

Your turn — F = ma

Circular motion SUPP

An object moving in a circle is constantly changing direction, so its velocity changes — it is accelerating. A force points toward the centre to keep it on the circle.

The moment of a force

A moment is the turning effect of a force about a pivot:

When there is no resultant force and no resultant moment, an object is in equilibrium. The principle of moments: for a balanced beam, total clockwise moments = total anticlockwise moments.

Watch out: the distance is the perpendicular distance from the pivot to the line of the force. A force acting through the pivot has zero moment.

Your turn — moment

Centre of gravity & stability

The centre of gravity is the single point where an object's whole weight seems to act. You can find it for a flat lamina by hanging it freely from two points and using a plumb line.

Which is most stable?

Momentum, impulse & conservation SUPP

All of Topic 1.6 is Extended-only. Momentum measures "how hard it is to stop" a moving object — mass × velocity (a vector):

The principle of conservation of momentum: in a collision with no external force, total momentum before = after. Resultant force can also be written as the rate of change of momentum, F = Δp ÷ t.

Your turn — momentum

Energy stores & conservation

Energy may be stored as: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal). It is transferred between stores by forces (mechanical work), electric currents (electrical work), heating, and waves.

The principle of conservation of energy: energy cannot be created or destroyed — only transferred or stored.

Watch out: energy is never "used up" or "lost" — only dissipated (spread to the surroundings, usually by heating) so it is no longer useful. The total is always conserved.

Kinetic & gravitational equations SUPP

The energy in the kinetic store and the change in the gravitational potential store are (Extended only):

Because speed is squared, doubling the speed gives four times the kinetic energy — one reason braking distance grows so quickly.

Your turn — kinetic energy

Your turn — gravitational store

Work & power

Mechanical work done equals the energy transferred when a force moves through a distance:

Power is the rate of doing work or transferring energy:

One watt is one joule per second (1 W = 1 J/s).

Your turn — power

Efficiency & Sankey diagrams

In every transfer some energy is dissipated to the surroundings. Efficiency is the fraction that ends up useful:

Efficiency is always between 0 and 1 (0–100%) — you can never get more useful energy out than you put in.

Your turn — efficiency

Where our energy comes from

Useful energy — or generated electricity — comes from many resources. Many drive a boiler → turbine → generator:

• Fossil fuels & biofuels (chemical store, burned).
• Water — waves, tides, hydroelectric dams.
• Geothermal, nuclear fuel, and the Sun (solar cells for electricity; solar panels to heat water).

SUPP Radiation from the Sun is the source of almost all our resources (except geothermal, nuclear and tidal). The Sun's energy is released by nuclear fusion; research aims to harness fusion for power on Earth.

Trade-offs: fossil fuels are reliable but release CO₂. Renewables are cleaner, but solar/wind/tidal are intermittent. Compare on renewability, availability, reliability, scale and environmental impact.

Renewable or not?

Tap a resource, then tap the box it belongs in.

Pressure = force ÷ area

Pressure is the force acting per unit area:

Spreading a force over a large area gives low pressure (snowshoes, camel feet); concentrating it on a small area gives high pressure (a sharp knife, a drawing pin).

Your turn — pressure

Pressure beneath a liquid

The pressure inside a liquid increases with depth and with the liquid's density. The deeper you go, the more liquid weighs down on you:

Watch out: liquid pressure depends on depth and density only — not on the shape or width of the container, and not on the total amount of liquid.

Your turn — pressure in a liquid

The equations to know

You've covered all eight sub-areas of Cambridge IGCSE Physics Topic 1. Press Finish to see your score.