| Outcome | Relevant Syllabus Block | What You’ll Use Here |
|---|---|---|
| 1.1 – Identify and use SI units | Physical quantities & units | Tables 2 & 3, dimensional symbols |
| 1.2 – Apply dimensional analysis | All blocks (kinematics, dynamics, …) | Procedure (section 8) and worked examples |
| 1.3 – Propagate uncertainties | Uncertainty & error analysis | Section 7 |
| 1.4 – Use vectors correctly | Vectors (topic 1.4) | Section 6 |
| 2–10 – Apply equations in each physics topic | Kinematics, dynamics, …, particle physics | Expanded “Core equations” table (section 5) |
| Quantity | Symbol | SI Base Unit | Unit Symbol |
|---|---|---|---|
| Length | ℓ | metre | m |
| Mass | m | kilogram | kg |
| Time | t | second | s |
| Electric current | I | ampere | A |
| Thermodynamic temperature | T | kelvin | K |
| Amount of substance | n | mole | mol |
| Luminous intensity | Iv | candela | cd |
| Quantity | Symbol | Derived Unit (SI) | Unit Symbol | Base‑unit expression |
|---|---|---|---|---|
| Velocity | v | metre per second | m s⁻¹ | m s⁻¹ |
| Acceleration | a | metre per second squared | m s⁻² | m s⁻² |
| Force | F | newton | N | kg m s⁻² |
| Pressure | p | pascal | Pa | kg m⁻¹ s⁻² |
| Density | ρ | kilogram per cubic metre | kg m⁻³ | kg m⁻³ |
| Energy / Work | E, W | joule | J | kg m² s⁻² |
| Power | P | watt | W | kg m² s⁻³ |
| Electric charge | Q | coulomb | C | A s |
| Voltage | V | volt | V | kg m² s⁻³ A⁻¹ |
| Resistance | R | ohm | Ω | kg m² s⁻³ A⁻² |
| Capacitance | C | farad | F | kg⁻¹ m⁻² s⁴ A² |
| Magnetic flux | Φ | weber | Wb | kg m² s⁻² A⁻¹ |
| Magnetic flux density | B | tesla | T | kg s⁻² A⁻¹ |
| Inductance | L | henry | H | kg m² s⁻² A⁻² |
| Frequency | f | hertz | Hz | s⁻¹ |
| Angular frequency | ω | radian per second | rad s⁻¹ | s⁻¹ |
| Momentum | p | kilogram metre per second | kg m s⁻¹ | kg m s⁻¹ |
| Impulse | J | newton second | N s | kg m s⁻¹ |
| Stress | σ | pascal | Pa | kg m⁻¹ s⁻² |
| Strain | ε | dimensionless | – | – |
| Intensity (light) | I | lux | lx | cd sr m⁻² |
When performing dimensional analysis we replace each physical quantity by its dimensional symbol:
[L][M][T][I][Θ][N][J][AB] = [A][B][A/B] = [A][B]⁻¹[Aⁿ] = [A]ⁿd/dt adds [T]⁻¹; for integrals, ∫dt adds [T].| Topic | Equation | Dimensional Form | Homogeneous? |
|---|---|---|---|
| Kinematics | v = u + at | [L][T]⁻¹ = [L][T]⁻¹ + [L][T]⁻²·[T] | Yes |
| s = ut + ½at² | [L] = [L][T] + [L][T]⁻²·[T]² | Yes | |
| a = (v – u)/t | [L][T]⁻² = ([L][T]⁻¹)/[T] | Yes | |
| Dynamics | F = ma | [M][L][T]⁻² = [M]·[L][T]⁻² | Yes |
| p = mv (momentum) | [M][L][T]⁻¹ = [M]·[L][T]⁻¹ | Yes | |
| J = FΔt (impulse) | [M][L][T]⁻¹ = [M][L][T]⁻²·[T] | Yes | |
| Δp = FΔt (impulse‑momentum theorem) | [M][L][T]⁻¹ = [M][L][T]⁻²·[T] | Yes | |
| Forces, Density & Pressure | Weight: W = mg | [M][L][T]⁻² = [M]·[L][T]⁻² | Yes |
| Pressure: p = F/A | [M][L]⁻¹[T]⁻² = [M][L][T]⁻²·[L]⁻² | Yes | |
| Density: ρ = m/V | [M][L]⁻³ = [M]·[L]⁻³ | Yes | |
| Work, Energy & Power | W = Fd cosθ | [M][L]²[T]⁻² = [M][L][T]⁻²·[L] | Yes |
| Gravitational PE: E_g = mgh | [M][L]²[T]⁻² = [M]·[L][T]⁻²·[L] | Yes | |
| Kinetic E: E_k = ½mv² | [M][L]²[T]⁻² = [M]·([L][T]⁻¹)² | Yes | |
| Power: P = W/t = Fv | [M][L]²[T]⁻³ = [M][L][T]⁻²·[L][T]⁻¹ | Yes | |
| Efficiency: η = (useful E / input E) ×100 % | dimensionless (no units) | Yes | |
| Deformation of Solids | Hooke’s law: F = kx | [M][L][T]⁻² = [M][T]⁻²·[L] | Yes |
| Stress: σ = F/A | [M][L]⁻¹[T]⁻² = [M][L][T]⁻²·[L]⁻² | Yes | |
| Strain: ε = ΔL/L | dimensionless | Yes | |
| Waves | Wave speed: v = fλ | [L][T]⁻¹ = [T]⁻¹·[L] | Yes |
| Angular frequency: ω = 2πf | [T]⁻¹ = [T]⁻¹ | Yes | |
| Wave equation (1‑D): ∂²y/∂t² = v²∂²y/∂x² | [L][T]⁻² = [L]²[T]⁻²·[L]⁻² | Yes | |
| Intensity–Amplitude: I = ½ρvω²A² | [M][T]⁻³ = [M][L]⁻³·[L][T]⁻¹·[T]⁻²·[L]² | Yes | |
| Superposition | Allowed wavelengths: λ = 2L/n | [L] = [L]/(dimensionless) | Yes |
| Fundamental frequency of a string: f₁ = v/2L | [T]⁻¹ = ([L][T]⁻¹)/[L] | Yes | |
| Electricity & DC Circuits | Ohm’s law: V = IR | [M][L]²[T]⁻³[I]⁻¹ = [I]·[M][L]²[T]⁻³[I]⁻² | Yes |
| Power: P = IV | [M][L]²[T]⁻³ = [I]·[M][L]²[T]⁻³[I]⁻¹ | Yes | |
| Resistance of a uniform wire: R = ρℓ/A | [M][L]²[T]⁻³[I]⁻² = [M][L]³[T]⁻³[I]⁻²·[L]·[L]⁻² | Yes | |
| Capacitance: C = Q/V | [I]²[T]⁴[M]⁻¹[L]⁻² = [I][T]/[M][L]²[T]⁻³[I]⁻¹ | Yes | |
| Time constant: τ = RC | [T] = [M][L]²[T]⁻³[I]⁻²·[M]⁻¹[L]⁻²[T]⁴[I]² | Yes | |
| Magnetism | Magnetic flux: Φ = BA | [M][L]²[T]⁻²[I]⁻¹ = [M][T]⁻²[I]⁻¹·[L]² | Yes |
| Force on a current‑carrying conductor: F = BIL sinθ | [M][L][T]⁻² = [M][T]⁻²[I]⁻¹·[I]·[L] | Yes | |
| Induced emf (Faraday): ε = –dΦ/dt | [M][L]²[T]⁻³[I]⁻¹ = [M][L]²[T]⁻²[I]⁻¹·[T]⁻¹ | Yes | |
| Particle Physics | E = mc² | [M][L]²[T]⁻² = [M]·([L][T]⁻¹)² | Yes |
| Relativistic momentum: p = E/c | [M][L][T]⁻¹ = [M][L]²[T]⁻²·[L]⁻¹[T] | Yes |
In experimental work (Paper 3 & 5) the propagation of uncertainties follows the same algebraic rules as units:
Equation: \(F = ma\)
\[ [F]=[M][L][T]^{-2},\qquad [m]=[M],\qquad [a]=[L][T]^{-2} \]Since \([M][L][T]^{-2}= [M]\times[L][T]^{-2}\), the equation is homogeneous.
Equation: \(E_{k}= \tfrac12 mv^{2}\)
\[ [E_{k}]=[M][L]^{2}[T]^{-2},\qquad [m]=[M],\qquad [v]^{2}=([L][T]^{-1})^{2}=[L]^{2}[T]^{-2} \]Both sides give \([M][L]^{2}[T]^{-2}\); the equation is dimensionally consistent.
Incorrect proposal: \(v = \dfrac{f}{\lambda}\)
\[ [v]=[L][T]^{-1},\qquad [f]=[T]^{-1},\qquad [\lambda]=[L] \]Right‑hand side gives \([T]^{-1}[L]^{-1}\), which is \([L]^{-1}[T]^{-1}\) – the opposite of the required dimensions. The correct form is \(v = f\lambda\).
Equation: \(\tau = RC\)
\[ [R]=[M][L]^{2}[T]^{-3}[I]^{-2},\qquad [C]=[M]^{-1}[L]^{-2}[T]^{4}[I]^{2} \] \[ [RC]=[M][L]^{2}[T]^{-3}[I]^{-2}\times[M]^{-1}[L]^{-2}[T]^{4}[I]^{2}= [T] \]Both sides have units of seconds – the equation is homogeneous.
Equation: \(F = kx\)
\[ [F]=[M][L][T]^{-2},\qquad [k]=[M][T]^{-2},\qquad [x]=[L] \] \[ [kx]=[M][T]^{-2}\times[L]=[M][L][T]^{-2} \]Units match, confirming the correctness of the constant’s dimensions.
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