1.1.1 — Describe the use of rulers and measuring cylinders to find a length or a volume

Measuring Length with a Ruler

A ruler is simple, but accurate measurement requires good technique.

Steps for accurate measurement:

• Place the object against the ruler — don’t hold it in mid-air.
• Start at the zero mark, not the edge of the ruler (the edge may be worn).
• Read at eye level to avoid parallax error — the illusion that the measurement is different when viewed from an angle.
• Read to the nearest millimetre (mm).

Real-world example:

Engineers measuring the length of screws or parts for a machine must avoid parallax errors, or the parts will not fit correctly.

Measuring Volume with a Measuring Cylinder

Used for liquids or irregular solids.

Steps for accurate measurement:

• Place the measuring cylinder on a flat surface.
• Get your eyes level with the liquid’s surface.
• Read from the bottom of the meniscus (the curved surface of the liquid).

For irregular solids, use the displacement method:

• Note the initial water level.
• Submerge the object.
• New volume – initial volume = volume of the object.

Real-world example:

Pharmacists must measure liquid medicines accurately. Reading above the meniscus could lead to overdosing or underdosing.

1.1.2 — Describe how to measure a variety of time intervals using clocks and digital timers

Time intervals range from minutes to fractions of a second, and we select tools depending on precision needed.

Common timing devices:

• Clocks / stopwatches: for seconds and minutes.
• Digital timers / smartphone timers: for fast events, accurate to 0.01 s or 0.001 s.
• Light gates (in labs): for very short intervals (not required but useful context).

Good practice when starting and stopping by hand:

• Anticipate the start/stop — human reaction time adds a delay of about 0.1–0.3 s.
• Repeat several times and take an average.

Real-world example:

Athletics uses electronic timing because human reaction time would introduce large errors in sprint races.

1.1.3 — Determine an average value for a small distance and for a short interval of time by measuring multiples (including the period of oscillation of a pendulum)

When distances or times are very small, measuring once is unreliable. Instead, measure many repetitions.

Examples:

1. Measuring a very small distance

Suppose you want the thickness of one sheet of paper:

• Measure the thickness of 100 sheets.
• Divide by 100.

This reduces error by averaging out tiny uncertainties.

2. Measuring a short time: the period of a pendulum

A pendulum swings too quickly to time one oscillation accurately.

Steps:

• Time 20 oscillations using a stopwatch.
• Divide total time by 20 → period, T.

Real-world example:

Scientists measuring microscopic distances or tiny time intervals always measure multiples — the same principle used by astronomers timing pulsars or engineers measuring vibration frequencies.

Supplement Content

1.1.4 — Understand that a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction

Scalar quantities

Have magnitude only (size).

Example: “10 m” — just a length, no direction.

Vector quantities

Have magnitude AND direction.

Example: “10 m east” — the direction changes the meaning completely.

Real-world example:

A weather report giving wind speed only is incomplete — wind direction is crucial for pilots and sailors.

1.1.5 — Know that the following quantities are scalars: distance, speed, time, mass, energy and temperature

These quantities do not depend on direction:

• Distance
• Speed
• Time
• Mass
• Energy
• Temperature

Check for understanding:

Why is speed a scalar but velocity a vector? → Because speed has no direction; velocity includes direction.

1.1.6 — Know that the following quantities are vectors: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength

These quantities require direction:

• Force
• Weight (force due to gravity)
• Velocity
• Acceleration
• Momentum
• Electric field strength
• Gravitational field strength

Real-world example:

When two people push a car, the forces must be in the same direction to be effective. If they push at right angles, the car moves in a completely different direction — this is vector addition in real life.

1.1.7 — Determine, by calculation or graphically, the resultant of two vectors at right angles, limited to forces or velocities only

You must be able to find the combined effect (resultant) of two perpendicular vectors, like:

• Two forces acting at 90°
• A boat moving across a river with a current
• An aircraft flying with a crosswind

Method 1: Pyth agoras (when vectors are at right angles)

If forces F₁ and F₂ are perpendicular:

$R = \sqrt{F_1^2 + F_2^2}$