• 1.1 Physical quantities and measurement techniques

• 1(a) Units
• 1(c) Forces, movement, shape and momentum

• 1.1 Forces and their interactions
• 6.1 Experimental and investigative skills
• 6.3 Mathematical requirements

• Describe the use of rulers and measuring cylinders to find a length or a volume.
• Describe how to measure a variety of time intervals using clocks and digital timers.
• 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.
• Understand that a scalar quantity has magnitude only and a vector quantity has magnitude and direction.
• Know that distance, speed, time, mass, energy and temperature are scalars.
• Know that force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength are vectors.
• Determine, by calculation or graphically, the resultant of two vectors at right angles, limited to forces or velocities.
• Identify independent, dependent and control variables, and describe how to design a fair test.
• Distinguish a hypothesis from a prediction, carry out a risk assessment, and explain the difference between repeatable, reproducible and valid results.

• Section 2 covers SI units and prefixes.
• Section 3 covers measuring length and volume.
• Section 4 covers measuring time.
• Section 5 covers the multiple-measurement technique for small quantities.
• Sections 6–7 cover scalars and vectors.
• Section 8 covers finding a resultant of two perpendicular vectors.
• Sections 9–11 consolidate with worked examples, misconceptions and a summary.
• Section 13 covers planning and evaluating investigations: variables, fair tests, hypotheses and predictions, risk assessment, and repeatability, reproducibility and validity.

• Convert to SI units before substituting, not afterwards. Metres, kilograms and seconds go into the equation; anything else invites an error.
• Square the conversion factor for areas and cube it for volumes. $1\text{cm}=10^{-2}\text{m}$, so $1{\text{cm}}^2=10^{-4}{\text{m}}^2$ and $1{\text{cm}}^3=10^{-6}{\text{m}}^3$.

• Place the object alongside the scale, with one end at a clear graduation.
• Read at eye level, looking straight down on the mark, to avoid parallax error.
• A metre rule reads to the nearest $1\text{mm}$.

• Stand the cylinder on a level surface.
• Read at eye level, level with the liquid surface.
• Read the bottom of the meniscus — the curved surface of the liquid.

• A stop-watch is started and stopped by hand, so each reading carries the operator's reaction time — typically around $0.2\text{s}$ at each end.
• A digital timer triggered by light gates starts and stops automatically, removing reaction time entirely.
• A digital display shows more figures, but more figures do not by themselves mean a more accurate result — a hand-started digital watch is still limited by the hand.

1. 1
   Set the pendulum swinging through a small angle.
2. 2
   Start the stop-watch as the bob passes the centre of its swing, not at the end.
3. 3
   Count 20 complete oscillations and record the total time $t$.
4. 4
   The period is $T=\frac{t}{20}$.
5. 5
   Repeat and take a mean.

• Distance (scalar) and displacement (vector). Walk 3 m east then 3 m west and you have travelled a distance of 6 m but have a displacement of zero.
• Speed (scalar) and velocity (vector). A car going round a roundabout at a steady $30\text{km/h}$ has constant speed but changing velocity, because its direction keeps changing.
• Mass (scalar) and weight (vector). Mass is a quantity of matter; weight is a force, and forces always have direction.

• Same direction → resultant $3+4=7\text{N}$.
• Opposite directions → resultant $4-3=1\text{N}$.
• At right angles → resultant $\sqrt{3^2+4^2}=5\text{N}$.

1. 1
   Magnitude: $R=\sqrt{6.0^2+8.0^2}=\sqrt{36+64}=\sqrt{100}=10.0\text{N}$.
2. 2
   Direction: $\tan \theta =\frac{8.0}{6.0}=1.333$, so $\theta =53^{\circ }$.
3. 3
   Answer: $10.0\text{N}$ at $53^{\circ }$ north of east.

• Calculation is exact and quicker. Use it whenever the vectors are at right angles.
• Scale drawing works for any angle, not only $90^{\circ }$, but its accuracy is limited by how well you can draw and measure.
• If a question says 'by scale drawing', you must draw — a calculated answer will not score.

1. 1
   (a) One sheet is about $0.1\text{mm}$ thick, which is smaller than the $1\text{mm}$ resolution of the rule, so the uncertainty is larger than the quantity being measured.
2. 2
   (b) Measure the total thickness of a large known number of sheets pressed together, then divide by the number of sheets.
3. 3
   This spreads the same $1\text{mm}$ uncertainty across many sheets, so the uncertainty per sheet is far smaller.
4. 4
   (c) $\frac{25}{250}=0.10\text{mm}$.

1. 1
   (a) $T=\frac{28.4}{20}=1.42\text{s}$.
2. 2
   (b) One oscillation is too short to time reliably, because the reaction time of the operator would be a large fraction of the reading.
3. 3
   Timing 20 and dividing spreads that error across 20 oscillations, so the error per oscillation is much smaller.
4. 4
   (c) Start as the bob passes the centre of the swing, because it is moving fastest there, so the instant of passing is easiest to judge.

1. 1
   The two velocities are at right angles, so use Pythagoras: $v=\sqrt{4.0^2+3.0^2}$.
2. 2
   $v=\sqrt{16+9}=\sqrt{25}=5.0\text{m/s}$.
3. 3
   Direction: $\tan \theta =\frac{3.0}{4.0}=0.75$, so $\theta =37^{\circ }$.
4. 4
   Resultant velocity $=5.0\text{m/s}$ at $37^{\circ }$ east of north.

1. 1
   (a) The average velocity is zero.
2. 2
   Velocity is a vector based on displacement, and the car returns to its start, so its displacement for the lap is zero — even though the distance travelled is a full lap.
3. 3
   (b) It is accelerating, because its direction is continually changing, so its velocity changes even though its speed is constant.

• Convert to SI units before substituting; square the factor for areas and cube it for volumes.
• Read a measuring cylinder at the bottom of the meniscus, at eye level, on a level surface.
• For small quantities, measure many and divide — and explain that this reduces the uncertainty per item.
• Time 20 oscillations and start from the centre of the swing.
• Learn both lists of scalars and vectors — they are directly examinable.
• For perpendicular vectors use $R=\sqrt{A^2+B^2}$ and $\tan \theta =\frac{B}{A}$.
• Always give a vector answer as magnitude and direction, with the direction stated relative to something.
• If a question says by scale drawing, draw it and state your scale.

• Common misconception: $1{\text{cm}}^3=10^{-2}{\text{m}}^3$. It is $10^{-6}{\text{m}}^3$ — the factor is cubed.
• Common misconception: a digital timer is always more accurate. If it is hand-started it still carries reaction time.
• Common misconception: more decimal places means more accuracy. Precision and accuracy are different things.
• Common misconception: timing many oscillations reduces the timing error itself. The error is the same; it is shared between more oscillations.
• Common misconception: the stop-watch should be started at the end of the swing. Start at the centre, where the bob moves fastest.
• Common misconception: mass and weight are the same. Mass is a scalar quantity of matter; weight is a vector force.
• Common misconception: constant speed means no acceleration. Changing direction is also an acceleration.
• Common misconception: $3\text{N}$ and $4\text{N}$ always give $7\text{N}$. Only if they act in the same direction.
• Common misconception: parallax error is removed by repeating. It is systematic — only fixing the technique removes it.

Do not name equipment without explaining why. Choose an instrument whose scale is fine enough for the quantity, avoid parallax by reading at eye level, repeat readings, and explain how an average or a longer measured interval reduces percentage uncertainty.

Repeating readings is useful only for random variation. It does not remove a zero error, parallax error or a consistently poor method. First identify the largest likely source of uncertainty, then improve that part of the method.

• Hazard: a glass measuring cylinder falling and breaking. Risk: a cut from broken glass. Precaution: use a plastic cylinder, or keep it away from the edge of the bench.
• Hazard: a swinging pendulum bob. Risk: impact injury or knocking apparatus over. Precaution: clamp the stand securely and keep a clear space around the swing.

• Measure length with a rule and volume with a measuring cylinder, reading at eye level to avoid parallax error; read the bottom of the meniscus.
• Find the volume of an irregular solid by displacement.
• Time intervals with clocks, stop-watches or digital timers; hand-operated timing carries reaction time error.
• For a small distance or short time, measure a large number together and divide.
• The period of a pendulum is the time for one complete oscillation: time 20 and divide, starting from the centre of the swing.
• A scalar has magnitude only; a vector has magnitude and direction.
• Scalars: distance, speed, time, mass, energy, temperature.
• Vectors: force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.
• For two vectors at right angles: $R=\sqrt{A^2+B^2}$ and $\tan \theta =\frac{B}{A}$.
• Alternatively find the resultant graphically, by drawing the vectors head to tail to scale.
• Always give a vector as magnitude and direction.
• A fair test changes only the independent variable, measures the dependent variable, and holds every control variable constant.
• A hypothesis explains; a prediction states what will happen. Results are repeatable if the same experimenter gets the same answer again, reproducible if someone else does too using a different method, and valid only if the procedure genuinely answers the question asked.