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Class 9–10 · Physics
Physical quantities and measurement
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Physical quantities and measurement
Lessons in this chapter
Lessons
1Physics and scientific inquiry
Physics studies matter, energy, space and time. Test a hypothesis by changing one relevant variable while controlling others, then repeat measurements. Galileo's experiments, Newtonian mechanics, relativity and quantum theory progressively extended our models. Evidence can refine an earlier explanation.
Key relationship
observation → hypothesis → controlled test → analysis → replication
Worked example
Pendulum: change length; keep mass and small release angle fixed; time 20 oscillations at each length.
Next lesson →2Base and derived quantities
Measurable properties are physical quantities. SI base units are metre, kilogram, second, ampere, kelvin, mole and candela. Area and velocity are derived from base quantities. A measured value needs both a number and its unit.
Key relationship
area = length × width; velocity unit = m/s
Worked example
3 m × 2 m = 6 m²
Next lesson →3Units and scientific notation
Prefixes express powers of ten. Convert all inputs to compatible units before substitution. Square a length conversion for area and cube it for volume. Scientific notation separates a coefficient from its power of ten.
Key relationship
1 cm² = 10⁻⁴ m²; 1 cm³ = 10⁻⁶ m³
Worked example
72 km/h = 72 × 1000/3600 = 20 m/s; 0.00045 = 4.5 × 10⁻⁴
Next lesson →4Dimensions
Dimensions describe the powers of base quantities. Terms added together must have matching dimensions. Dimensional analysis detects many errors, but cannot establish dimensionless numerical factors such as ½.
Key relationship
[v] = LT⁻¹; [a] = LT⁻²; [F] = MLT⁻²; [energy] = ML²T⁻²
Worked example
[ut] = LT⁻¹T = L; [at²] = LT⁻²T² = L
Next lesson →5Ruler and vernier calipers
Read a scale with the eye perpendicular to avoid parallax. Add the matching vernier division multiplied by the least count to the main-scale reading. For a direct vernier, its constant is the difference between one main-scale and one vernier division. Subtract signed zero error.
Key relationship
reading = main scale + matching division × least count; corrected = observed − zero error
Worked example
2.30 + 6 × 0.01 = 2.36 cm; zero error +0.02 cm ⇒ 2.34 cm
Next lesson →6Micrometer screw gauge
Pitch is the advance per full turn. Divide it by the circular-scale divisions to find the least count. Use the ratchet for consistent light pressure and measure a wire at several positions. Apply zero correction to the combined linear and circular readings.
Key relationship
least count = pitch/divisions; reading = linear scale + circular reading × least count
Worked example
0.5/50 = 0.01 mm; 1.5 + 23 × 0.01 = 1.73 mm
Next lesson →7Error and uncertainty
Calibration problems cause systematic error; repeat readings reveal random variation. Averaging can reduce random effects but does not correct a consistent offset. Absolute uncertainty carries the measured unit; relative uncertainty compares it with the measured magnitude.
Key relationship
percentage uncertainty = absolute uncertainty/measured value × 100%
Worked example
(20.0 ± 0.1) cm ⇒ (0.1/20.0) × 100 = 0.5%
Next lesson →8Significant figures
Leading zeros are not significant; internal zeros and precision-indicating trailing zeros are. Round products to the least number of significant figures, and sums to the least precise decimal place. Keep extra digits during calculations and round the final result.
Key relationship
0.00450 has 3 significant figures
Worked example
12.3 cm + 0.45 cm = 12.75 cm ≈ 12.8 cm; 2.0 × 3.12 ≈ 6.2
Next lesson →Check your understanding
Try answering first, then open the question to compare your reasoning.
1. Convert 1 mm² to m².
(10⁻³)² = 10⁻⁶ m²
2. Reading 2.45 cm, zero error +0.03 cm. Corrected reading?
2.45 − 0.03 = 2.42 cm
3. What are the dimensions of force?
F = ma ⇒ MLT⁻²
4. Pitch 1 mm, 100 divisions. Least count?
1/100 = 0.01 mm
5. Percentage uncertainty of 50 ± 1 cm?
1/50 × 100 = 2%
Sources and scope
Original GetReady teaching notes. The 13 core chapters follow the existing site sequence. Physics to save life is an explicitly labelled older-edition supplement. Check your current book and board instructions for examination scope. Illustrations are schematic. Unless stated otherwise, use g = 9.8 m/s². A physics teacher should review content and edition coverage before it is relied on.