Experimental skills

The **smallest division** it can read (e.g. 1 mm on a metre rule, 0.01 mm on a micrometer). Finer resolution → smaller uncertainty.

A wrong reading caused by looking at the scale **from an angle** instead of straight on (at eye level).

The instrument **doesn't read zero** when it should, so every reading is off by that fixed amount.

Metre rule **1 mm**, vernier caliper **0.1 mm**, micrometer screw gauge **0.01 mm**.

Pick a resolution that is a **small fraction** of the quantity, so the fractional uncertainty stays small.

Measure a **stack of N sheets** and divide by N — the value **and** its absolute uncertainty both divide by N.

The fixed reaction-time uncertainty applies to the whole run, so dividing the total by 10 divides that absolute uncertainty by 10.

Add the **fractional** uncertainties: $\tfrac{\Delta y}{y} = \tfrac{\Delta a}{a} + \tfrac{\Delta b}{b} + \tfrac{\Delta c}{c}$ (given in the data booklet).

Multiply the fractional uncertainty by the power: $\tfrac{\Delta y}{y} = |n|\,\tfrac{\Delta a}{a}$ (given in the data booklet).

Add the **absolute** uncertainties: $\Delta y = \Delta a + \Delta b$ (derived, not in the booklet).

Read the **bottom of the meniscus** at **eye level** to avoid a parallax error.

A **justification by its resolution** — match the instrument's smallest division to the quantity, don't just name it.

Any quantity that could change the result, so it is **kept the same** while only the independent variable is changed.

At least **five** values of the independent variable, spread as **widely** as is practical, each repeated.

**t = number of frames ÷ frame rate**; then speed = distance ÷ t.

A ± amount in the **same unit** as the measurement (e.g. 12.4 ± 0.2 cm → Δx = 0.2 cm).

**Absolute uncertainty ÷ the value** — a plain number with no unit (Δx/x).

**Fractional × 100%** = (Δx/x) × 100%.

**± half the smallest scale division** (a mm ruler → ±0.5 mm; a 0.01 g balance → ±0.005 g).

**± half the range** = ½ × (largest − smallest reading).

**Add the ABSOLUTE uncertainties:** Δy = Δa + Δb.

**Add the FRACTIONAL (or %) uncertainties:** Δy/y = Δa/a + Δb/b + Δc/c. (Given in the data booklet.)

**Multiply the fractional uncertainty by |n|:** Δy/y = |n·Δa/a|. (Given in the data booklet.)

**Multiply by the value:** Δy = (Δy/y) × y.

Round the **uncertainty to 1 s.f.**, then round the **value to the same decimal place** (e.g. 2.643 ± 0.087 → 2.64 ± 0.09).

**Fractional or percentage** — then convert back to absolute at the end.

Repeat it if possible; otherwise **leave it out** of the mean and the range, and give the reason.

It **halves** it (a power of ½): √P has half the % uncertainty of P.

Turn the % into an **absolute** value of the plotted quantity; draw that much **above and below** the point.

The single **straight line** drawn as close as possible to all the plotted points, with roughly as many points above it as below. You read the physics off this line.

The **uncertainty** in that measurement — the true value could lie anywhere along the bar.

Pick **two far-apart points ON the line** and compute **rise ÷ run**: $m = \Delta y / \Delta x$. Use the line, not the data points.

Draw the **steepest** and **shallowest** straight lines that still pass through all the error bars, then $\Delta m = (m_{\max} - m_{\min}) / 2$.

The **fractional** uncertainties add: $\Delta y/y = \Delta a/a + \Delta b/b + \Delta c/c$. **Given** in the data booklet.

Multiply the fractional uncertainty by the size of the power: $\Delta y/y = |n|\,\Delta a/a$. **Given** in the data booklet.

The **absolute** uncertainties add: $\Delta y = \Delta a + \Delta b$. Built from the booklet rules.

A relationship between the two plotted quantities — e.g. a **spring constant**, a **speed** (distance–time), or a **refractive index** (depending on what is plotted).

The value of y when x = 0 — often a physical quantity, or, if it should be zero, a sign of a **systematic offset** (zero error).

The best-fit line **averages out random scatter** across many readings, giving a more reliable value and letting you spot anomalies and offsets.

Usually **one** significant figure, and round the value to the same decimal place as the uncertainty.

One **smooth curve** through (or close to) every error bar, with the points balanced either side; never dot to dot.

Extending the line or curve **beyond the plotted data**, e.g. back to the axis, to read a value such as an intercept.

From the **bottom of the first** error bar to the **top of the last**, passing through every bar.

**Re-plotting a curved law as a straight line** by choosing the right quantity for each axis (e.g. P against 1/V, or d against √P).

**Y = mX + c** — match your two plotted quantities to Y and X; the gradient m and intercept c are physics quantities.

The two plotted quantities are **directly proportional**.

The relationship is **linear but NOT directly proportional** (there is a non-zero intercept c).

Check the **ratio Y/X is constant** across the rows. Different ratios → not proportional.

**y (up) against x² (across)** — then the gradient is k.

**y (up) against √x (across)** — then the gradient is k.

A **physics quantity** (a constant in the law) — quote it **with units**, never 'just a number'.

Add **fractional** uncertainties: Δy/y = Δa/a + Δb/b + Δc/c.

Multiply the fractional uncertainty by |n|: Δy/y = |n·Δa/a| (e.g. ×½ for a square root).

A straight line has one gradient you can read directly; a curve has a changing slope you cannot read as a single value.

Plot **ln y against x**: a straight line with gradient **−k** and intercept **ln A**.

The **power n** in y = k xⁿ (the intercept is log k).

Check that the **halving time is constant** (equal fractions lost in equal times).

A reading clearly **out of line** with the others (a one-off mistake) — discard it before averaging.

To reduce **random** uncertainty — the chance scatter up and down partly **cancels**, so the mean is more reliable.

**No** — a systematic error shifts every reading the same way. Fix the instrument or method (e.g. zero it).

Random = readings **scatter** around the true value (cured by averaging). Systematic = all readings **shifted** one way (not cured by averaging).

Balancing the **fundamental SI units** (kg, m, s, A) on both sides of an equation — to find an unknown power or state a constant's units.

Divide the **y-axis units by the x-axis units** (gradient = rise ÷ run), then simplify.

Balance the **base units one at a time** — each base unit (kg, m, s) gives one equation for the powers.

**kg m s⁻²** (the newton, N = kg m s⁻²).

**kg m² s⁻²** (the joule, J = N m = kg m² s⁻²).

Add the **fractional** uncertainties: $\dfrac{\Delta y}{y} = \dfrac{\Delta a}{a} + \dfrac{\Delta b}{b} + \dfrac{\Delta c}{c}$.

Add the **absolute** uncertainties: $\Delta y = \Delta a + \Delta b$ (it's a derived rule, not always printed).

Multiply the fractional uncertainty by $|n|$: $\dfrac{\Delta y}{y} = |n|\,\dfrac{\Delta a}{a}$.

As an **intercept** where the law predicts the line passes through the origin (every point shifted by the same amount).

Check whether the **accepted value** lies inside **value ± uncertainty**.

Any two: a **wider range** and more values; **even spacing**; repeats; a calibrated/zeroed instrument; a sensor instead of hand timing.