Important Formulas & Units

Standard Unit Conventions:

• Unit Names: Always lowercase (e.g., newtons, joules, volts, kilograms).

• Symbols (Namesakes): Uppercase if named after a physicist (e.g., $J$ for joules, $V$ for volts).

• Other Symbols: Lowercase (e.g., $kg$ for kilograms).

• Typography: Variables and constants must be italicized in equations (e.g., $(v = u + at)$).

Mechanics

• Area ($a$): metres squared ($m^2$)

• Volume ($v$): metres cubed ($m^3$)

• Mass ($m$): kilogram ($kg$)

• Density ($ρ$): kilogram per metre cubed ($kg/m^3$)

  • Equation: $(ρ = \frac{m}{v})$

• Displacement ($s$): metre ($m$)

• Velocity ($v$): metre per second ($m/s$)

  • Equation: $(v = \frac{d}{t})$

• Acceleration ($a$): metre per second squared ($m/s^2$)

• Force ($F$): newton ($N$)

  • Equation: $(F = ma)$

• Momentum ($ρ$): $kg \ m/s$

  • Equation: $(ρ = mv)$

• Pressure ($p$): pascal ($Pa$)

  • Equation: $(p = \frac{F}{a})$

• Work ($W$) / Energy ($E$): joule ($J$)

  • Equation: $(W = Fs)$

• Power ($P$): watt ($W$)

  • Equation: $(P = \frac{W}{t})$

• Torque ($T$): newton metre ($N \ m$)

  • Equation: $(T = F \times d)$

• Angular Velocity ($ω$): radian per second ($rad/s$)

  • Equation: $(ω = \frac{θ}{t})$

Heat and Temperature

• Heat Capacity ($C$): joule per kelvin ($J/K$)

  • Equation: $(Q = C Δθ)$

• Specific Heat Capacity ($c$): $J/kg/K$

  • Equation: $(Q = mcΔθ)$

• Latent Heat ($l$): joule per kilogram ($J/kg$)

  • Equation: $(Q = ml)$

Waves, Sound and Light

• Frequency ($f$): hertz ($Hz$)

• Wavelength ($λ$): metres ($m$)

• Wave Velocity ($v$): metre per second ($m/s$)

  • Equation: $(v = fλ)$

• Intensity ($I$): watts per metre squared ($W/m^2$)

• Sound Intensity Level: decibels ($dB$)

Electricity

• Charge ($Q$): coulomb ($C$)

• Electric Field Strength ($E$): newtons per coulomb ($N/C$)

  • Equation: $(E = \frac{F}{Q})$

• Potential Difference ($V$): volts ($V$)

  • Equation: $(W = VQ)$

• Capacitance ($C$): farads ($F$)

  • Equation: $(C = \frac{Q}{V})$

• Current ($I$): amperes ($A$)

  • Equation: $(I = \frac{Q}{t})$

• Resistance ($R$): ohm ($Ω$)

  • Equation: $(V = IR)$

• Resistivity ($ρ$): ohm-metre ($Ω \ m$)

  • Equation: $(ρ = \frac{RA}{l})$

• Magnetic Flux Density ($B$): tesla ($T$)

  • Equation: $(F = BIL)$

• Magnetic Flux ($Φ$): weber ($Wb$)

  • Equation: $(Φ = BA)$

Equations Summary for Exams

1. Mechanics and Motion

• Equations of Motion:

  • $(v = u + at)$

  • $(s = ut + \frac{1}{2} at^2)$

  • $(v^2 = u^2 + 2as)$

• Gravity and Pressure:

  • $(W = mg)$

  • $(P = ρgh)$

  • $(g = \frac{GM}{d^2})$

• Energy and Power:

  • $(E_k = \frac{1}{2} mv^2)$

  • $(E_p = mgh)$

  • $(Efficiency = \frac{Power \ Out}{Power \ In} \times 100)$

• Circular Motion & SHM:

  • $(v = rω)$

  • $(a = -ω^2 s)$

  • $(T = 2π \sqrt{l/g})$

2. Light and Optics

• Refraction:

  • $(n = \frac{sin \ i}{sin \ r})$

  • $(n = \frac{c}{v})$

• Lenses and Mirrors:

  • $(P = \frac{1}{f})$

  • $(\frac{H}{h} = \frac{v}{u})$

3. Modern Physics

• Mass-Energy: $(E = mc^2)$

• Photon Energy: $(E = hf)$ or $(E = \frac{hc}{λ})$

• Photoelectric Effect: $(hf = φ + \frac{1}{2}mv^2)$

• Radioactivity:

  • $(Rate = -λN)$

  • $(T_{1/2} = \frac{0.693}{λ})$

• Particle Physics:

  • Force on electron: $(F = Bev = \frac{mv^2}{r})$

  • Pair Production: $(γ \rightarrow e^- + e^+ + KE)$