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A-Level Physical quantities, units, measurement uncertainty and vector basics
What the A-Level syllabus expects for Physical quantities, units, measurement uncertainty and vector basics, and how to practise it.
What the syllabus expects
- Know from memory, and put to work, these base quantities of the SI system with their units: time (s), length (m), mass (kg), electric current (A), thermodynamic temperature (K), amount of substance (mol)
- Have at your command the metric prefixes and their symbols for scaling any base or derived unit up or down by powers of ten: tera (T), giga (G), mega (M), kilo (k), deci (d), centi (c), milli (m), micro (μ), nano (n), pico (p)
- Build derived units by multiplying or dividing the base SI units, and draw on the named units catalogued under 'Summary of Key Quantities, Symbols and Units' wherever they fit
- Confirm that an equation is dimensionally consistent by testing every term against the base SI units
- Produce sensible order-of-magnitude estimates for any quantity the course covers
- Explain what separates random errors from systematic ones and how each caps a measurement's precision and its accuracy
Scope: zero error is counted as a systematic error - Work out how uncertainty propagates into a derived quantity, either by summing the absolute or relative contributions or by substituting numerical bounds
Scope: no formal statistical treatment is expected; relative means fractional or percentage - Tell scalar quantities apart from vector ones and supply an example of both kinds
- Combine, or take the difference of, vectors that lie in one common plane
- Break a single vector down into a pair of components set at right angles
How it's examined
Questions on this topic most often ask you to find, state. About 4% of the past-paper style questions in Rae's bank for this subject sit in this topic.
Worked examples
Example 1 (2 marks)
(ii) Write the units of the permittivity of free space in terms of SI base units. units = ..............
Show the worked answer
From Coulomb's law F = Q²/(4πε₀r²), so ε₀ = Q²/(F·r²). Units: [Q²] = (A s)² = A² s²; [F·r²] = N·m² = (kg m s⁻²)·m² = kg m³ s⁻². Therefore ε₀ has units (A² s²)/(kg m³ s⁻²) = kg⁻¹ m⁻³ s⁴ A².
Example 2 (2 marks)
(b) The circular capacitor plates are found to have a diameter of 6.50 cm and to be separated by 5.42 mm. State which instrument is used for each measurement and give a reason. instrument for measuring the diameter .............. instrument for measuring the separation .............. reason ..............
Show the worked answer
Diameter (6.50 cm): use vernier calipers. Separation (5.42 mm): use a micrometer screw gauge. Reason: the micrometer reads to 0.01 mm, the fine resolution needed for the small plate separation, but its jaws/anvil gap (about 25 mm max) is too small to span the 6.50 cm diameter, so the larger diameter is measured with vernier calipers, which still give the 0.01 cm precision the quoted value requires.
Example 3 (4 marks)
A wire hangs vertically from a fixed point with a load on its lower end. Measurements give diameter d = 0.40 ± 0.02 mm and load F = 25.0 ± 0.5 N. The stress is σ = 4F/(πd²). Find σ and its uncertainty. [4]
Show the worked answer
Convert the diameter to metres: d = 0.40 mm = 0.40 × 10⁻³ m, so d² = (0.40 × 10⁻³)² = 1.6 × 10⁻⁷ m². Substitute into σ = 4F/(πd²): σ = (4 × 25.0)/(π × 1.6 × 10⁻⁷) = 100/(5.0265 × 10⁻⁷) = 1.98944 × 10⁸ ≈ 1.98 × 10⁸ N m⁻². For a quotient with a squared quantity, fractional uncertainties add, with the power as multiplier: Δσ/σ = ΔF/F + 2Δd/d. ΔF/F = 0.5/25.0 = 0.02 and 2Δd/d = 2 × 0.02/0.40 = 0.10, so Δσ/σ = 0.02 + 0.10 = 0.12. Δσ = 0.12 × 1.989 × 10⁸ = 0.239 × 10⁸ ≈ 0.2 × 10⁸ N m⁻² (uncertainty quoted to 1 s.f.). Quote σ to the same precision as its uncertainty: σ = (2.0 ± 0.2) × 10⁸ N m⁻².
More A-Level H2 Physics topics
Types of force, turning effects and conditions for equilibrium · Kinematics, uniformly accelerated motion, momentum and Newton's laws · Energy stores and transfers, work, kinetic and potential energy, fields, power and efficiency · Falling freely, the gravitational potential energy of a uniform field, and how air resistance changes the motion · Impulse and the conservation of momentum and energy · Kinematics of uniform circular motion and centripetal acceleration · all of A-Level H2 Physics