P1.1P1. Motion, Forces and Energy

Physical quantities and measurement techniques — Combined Science 0653 - Physics Revision Notes & Topical Questions

5 min read 10 parts Lesson 2 of 15 1 quiz

📚 Combined Science 0653 - Physics Hub / Topical Revision

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Lesson summary

P1.1 Physical quantities and measurement techniques — COMBINED SCIENCE notes: Measure length, volume and time accurately, reduce measurement error with multiple readings, and distinguish and combine scalar and vector quantities.Ruler — measures short lengths of a few centimetres …

Tape measure
Micrometer screw gauge
Measuring cylinder
Irregular solid
Unit conversions
Digital timers and stopwatches

Part 1 of 8Measuring length

Ruler

Ruler measures short lengths of a few centimetres to the nearest millimetre.
Start from the zero mark, or subtract the starting reading, and view the scale at 90° to avoid parallax error.

Tape measure

Tape measure measures longer lengths of tens of centimetres or more.

Micrometer screw gauge

Micrometer screw gauge measures very small lengths such as wire diameter to 0.01 mm.
Check for a zero error before use and subtract it from every reading.

Part 2 of 8Measuring volume

Measuring cylinder

Measuring cylinder measures the volume of a liquid.
Place it on a flat surface and read the scale level with the bottom of the meniscus at eye level.

Irregular solid

Irregular solid its volume equals the change in liquid level when it is submerged (displacement).

Unit conversions

1 cm³ = 1 ml and 1 m³ = 1 000 000 cm³.

Part-fill a measuring cylinder with water and record the volume V₁.

Lower the tied solid gently until it is fully submerged.

Record the new volume V₂.

Calculate the volume of the solid as V₂ − V₁.

Part 3 of 8Measuring time

Measuring time

Clocks

Clocks measure long time intervals.

Digital timers and stopwatches

Digital timers and stopwatches measure short time intervals.

Human reaction time

Human reaction time about 0.2 to 0.3 s for an alert person.
It adds a delay at both the start and the end of a manual timing.
It has a large effect on very short intervals because the percentage uncertainty is large.

Part 4 of 8Multiple readings

1Purpose

Purpose taking several measurements together improves precision and reduces the effect of measurement errors.

2Thickness of paper

Thickness of paper one sheet is too thin to measure precisely, so measure a stack of 100 sheets and divide by 100.

3Period of a pendulum

Period of a pendulum time 10 or 20 oscillations and divide by the number of oscillations.
The reaction-time error is shared between many oscillations, so the percentage uncertainty falls.

4Reference marker

Reference marker a line or dot at the equilibrium position of the pendulum makes it easier to start and stop the timer at the same point.

5Diameter of small objects

Diameter of small objects place identical objects in a row between two blocks, measure the total length and divide by the number of objects.

6Repeats

Repeats repeat each measurement and take the mean, which reduces the effect of random errors.

Part 5 of 8Scalar and vector quantities

Scalar

Scalar a quantity with magnitude (size) only.

Vector

Vector a quantity with both magnitude and direction.

Scalar	Vector
Distance	Displacement
Speed	Velocity
Mass	Weight and force
Time	Acceleration
Energy	Momentum
Temperature	Electric and gravitational field strength

Part 6 of 8Distance, displacement, speed and velocity

Distance

Distance the total length of the path travelled, with no direction, so it is a scalar.

Displacement

Displacement the straight-line distance between two points in a stated direction, so it is a vector.

Speed

Speed distance travelled per unit time, regardless of direction, so it is a scalar.

Velocity

Velocity speed in a given direction, so it is a vector.

Part 7 of 8Combining vectors by scale drawing

Combining vectors by scale drawing

Vector arrow

Vector arrow its length represents the magnitude and its direction shows the direction of the vector.

Resultant

Resultant the single vector with the same effect as the vectors it replaces.

Components

Components a force F has a vertical component F_V and a horizontal component F_H.

Choose a scale that fits the page, for example 1 cm = 1 N.

Draw the two vectors at right angles to each other.

Complete the rectangle.

Draw the resultant along the diagonal from the origin.

Measure its length and use the scale to find the magnitude.

Measure the angle with a protractor to find the direction.

Part 8 of 8Combining perpendicular vectors by calculation

Magnitude

Pythagoras' theorem gives F_R² = F₁² + F₂².
The vector diagram can be a labelled sketch and need not be to scale.

Direction

Direction tan θ = opposite ÷ adjacent, so θ = tan⁻¹(F₁ ÷ F₂).

Final answer

Final answer state both the magnitude and the direction of the resultant.

Course limit

Course limit resultants of two vectors are limited to forces and velocities.

Key terms

Term	Meaning
Meniscus	The curved surface of a liquid in a tube; the scale is read at the bottom of the curve.
Parallax error	A reading error caused by viewing a scale from an angle instead of at 90°.
Zero error	A non-zero reading when the true value is zero, subtracted from every reading.
Scalar	A quantity with magnitude only.
Vector	A quantity with both magnitude and direction.
Displacement	The straight-line distance between two points in a stated direction.
Resultant	The single vector with the same effect as two or more vectors acting together.
Reaction time	The delay of about 0.2 to 0.3 s between an event and a person's response to it.

Avoid these mistakes

Reading a measuring cylinder from above or below — read at eye level from the bottom of the meniscus.

Timing one short event by hand and trusting it — reaction time of about 0.2 s is large, so time many repeats and divide.

Treating speed as a vector — speed is a scalar, velocity is the vector with direction.

Forgetting the direction of a resultant — a vector answer needs magnitude and direction.

Ignoring a zero error — subtract it from every reading.

Last updated: 12 October 2026