ZIMSEC A Level · Physics · Form 5
SI base units and homogeneity
Base units: kg, m, s, A, K, mol, cd. Derived units are combinations: N = kg m s⁻², J = kg m² s⁻², W = kg m² s⁻³. An equation is homogeneous if both sides have the same base units – a check, not a proof, of correctness.
Errors and uncertainties
- Random errors scatter readings; reduced by repeating and averaging. Systematic errors shift all readings (zero error); not removed by averaging.
- Precision: how close repeated readings are. Accuracy: how close to the true value.
- Absolute uncertainty Δx; fractional Δx/x; percentage (Δx/x) × 100.
- Adding/subtracting quantities: add absolute uncertainties. Multiplying/dividing: add fractional uncertainties. Powers: multiply the fractional uncertainty by the power.
Worked example: The radius of a wire is (0.50 ± 0.01) mm. Find the percentage uncertainty in its cross-sectional area.
% uncertainty in r = 0.01/0.50 × 100 = 2%; A = πr², so % uncertainty in A = 2 × 2% = 4%
Vectors
Resolve a force F at angle θ into components F cos θ and F sin θ. Add vectors by components or by scale drawing.
Exam tip: Give final answers to the same number of significant figures as the least precise data.
Check yourself
- Show that the units of kinetic energy ½mv² are the same as those of work Fd.
- A length is measured as (20.0 ± 0.1) cm and another as (15.0 ± 0.1) cm. Find their difference with its uncertainty.
- Distinguish between random and systematic errors.
Show answers
- kg (m s⁻¹)² = kg m² s⁻²; N × m = kg m s⁻² × m = kg m² s⁻² – the same.
- (5.0 ± 0.2) cm
- Random errors scatter readings unpredictably; systematic errors shift all readings by the same amount in one direction.
Questions about this topic (0)
No questions about this topic yet.
Sign in or create a free account to join in.