IP Physics Notes (Upper Secondary, Year 3-4): 1) Physical Quantities, Units & Measurements

Quick recap -- Every measurement must carry a magnitude, a unit, and an honest statement about precision. Know your SI base units, keep prefixes on autopilot, eliminate zero/parallax errors, and present data with significant figures that match your apparatus.

Base & Derived Quantities

Seven base quantities anchor the SI system. Everything else is built from them.

Derived quantities follow from combining base units. Example: force \(F = ma\) gives \([F] = \text{kg} \cdot \text{m} \cdot \text{s}^{-2}\). Use dimensional homogeneity to check equations: both sides of \(s = ut + \tfrac{1}{2}at^2\) evaluate to metres, so the relation is dimensionally sound.

Prefixes & Scientific Notation

Memorise the common prefixes so you can convert without reaching for a calculator.

Switch comfortably between standard notation and scientific notation \(N \times 10^{n}\) where \(1 \leq N < 10\). Large: \(5.6 \times 10^{3}\ \text{m}\). Small: \(4.5 \times 10^{-3}\ \text{s}\). The coefficient's significant figures carry the precision--\(3.450 \times 10^{4}\) shows four significant figures, for instance.

Precision, Accuracy & Error Types

• Precision is about spread. Tight clustering of repeated readings = precise instrument/technique.
• Accuracy is about truth. Consistently hitting the accepted value = accurate measurement.
• Random errors (parallax, background fluctuations) scatter readings both above and below the true value. Average repeated trials to tame them.
• Systematic errors (zero error, miscalibrated apparatus) bias readings in one direction. Detect and correct using calibration checks or offset adjustments.

Significant Figures & Decimal Places

Report raw readings with all digits the instrument provides; state processed values with the limiting significant figures of the inputs.

• Non-zero digits are significant; zeros between significant digits count; trailing zeros count only when a decimal point is shown.
• Decimal places describe formatting; significant figures communicate precision. A balance reading 12.30 g has 4 s.f. and 2 d.p.
• When multiplying/dividing, round the final answer to the smallest number of significant figures used. When adding/subtracting, match the least precise decimal place.

Converting Units Systematically

1. Write the starting value with its unit, e.g. \(\pu{3.6 m}\).
2. Multiply by conversion fractions that equal one, e.g. \(\pu{1000 mm / 1 m}\).
3. Cancel units algebraically; the numbers follow the same multiplication.
4. Express the answer with the same significant figures as the original measurement.

Example: \(\pu{3.6 m} \times \dfrac{\pu{100 cm}}{\pu{1 m}} = \pu{3.6 \times 10^2 cm}\).

Measuring Length & Time Reliably

Common errors

• Parallax error: reading a scale from an angle. Fix: align your eye perpendicular to the scale; use mirrored scales when available.
• Zero error: instrument does not read zero when it should. Fix: record the offset and subtract/add it during processing.

Typical apparatus

• Meter rule: minimum uncertainty \(\pu{\pm 0.1 cm}\). Read at eye level.
• Vernier calipers: resolution \(\pu{0.01 cm}\). If the jaws show \(\pu{+0.02 cm}\) when closed, subtract 0.02 cm from all readings.
• Micrometer screw gauge: resolution \(\pu{0.01 mm}\). Watch for positive/negative zero error the same way.
• Stopwatch / light gate: for intervals under a second, repeat runs and average to reduce reaction-time error; for pendulum timing, measure multiple oscillations and divide.

Recording, Processing & Presenting Data

• Layout tables with headings that include units (e.g. \(\text{Time} / \pu{s}\)). Keep consistent decimal places within a column.
• When calculating derived values (e.g. \(v = \dfrac{s}{t}\)), propagate significant figures appropriately.
• Graphs: choose sensible scales, label axes with quantity and unit, plot using the largest portion of the grid, draw a best-fit line through the scatter, and use large triangles to determine gradient.
• Quote gradients/intercepts with the same precision as the data that produced them. Attach units to gradients (e.g. \(\pu{N.m-1}\)).

Precautions & Improvements

• Secure the apparatus (clamps, retort stands) to prevent drift during readings.
• Repeat measurements and look for outliers before averaging.
• For time-based experiments, start/stop at a consistent marker; for oscillations, time 10 or more cycles.
• Document ambient conditions (room temperature, zeroed instruments) so you can justify improvements when writing evaluations.

Mastering these fundamentals pays off in every later topic. The sooner you automate unit checks, prefix conversions, and data presentation habits, the more headspace you'll have for advanced mechanics and electromagnetism.