ORELA Physics (NT308) cheat sheet

SI base units are meter, kilogram, second, ampere, kelvin, mole and candela; derived units are products of these, e.g. 1 N = 1 kg·m/s², 1 J = 1 N·m, 1 W = 1 J/s, 1 V = 1 J/C.

Multiplication and division keep the smallest number of significant figures present in the data; addition and subtraction keep the smallest number of decimal places.

Percent error = |measured − accepted| ÷ accepted × 100%; percent difference compares two measurements when no accepted value exists.

Random error scatters repeated readings about the true value and shrinks when trials are averaged; systematic error offsets every reading (zero error, miscalibration) and averaging does not remove it.

Dimensional analysis: every term in a valid equation must reduce to the same combination of M, L, T, I, Θ, N, J; it verifies equations and predicts proportionality.

Linearizing data makes the constant of interest the slope: T² against L for a pendulum gives 4π²/g; V against I for a resistor gives R.

A hypothesis must be falsifiable; a law states a repeated regularity (usually with stated conditions), while a theory is a well-tested explanatory framework that predicts new phenomena.

History anchors: Galileo's kinematics, Newton's Principia (1687) unifying falling bodies with planetary orbits, Planck's 1900 quantum hypothesis, Einstein's 1905 relativity and photoelectric papers.

Precision describes reproducibility, resolution describes the smallest scale division of an instrument, and both differ from accuracy, which is closeness to the accepted value.

Constant-acceleration kinematics: v = v₀ + at, x = v₀t + ½at², v² = v₀² + 2ax; these fail whenever acceleration is not constant.

Projectile motion separates into constant horizontal velocity and vertical motion with a = −g (9.8 m/s²); the two components are independent and the object lands and peaks according to the vertical one.

ΣF = ma is a vector equation: resolve forces into perpendicular axes, and note that mass resists acceleration rather than causing it.

Friction: f_s ≤ μ_sN and f_k = μ_kN, always along the surface opposing relative sliding; N equals mg only in simple level cases, not on inclines or with extra vertical forces.

Work W = Fd cosθ counts only the force component along the displacement; the work-energy theorem states W_net = ΔKE, and power P = W/t = Fv cosθ.

Mechanical energy KE + PE is conserved when only conservative forces do work; friction moves mechanical energy into thermal energy.

Impulse J = FΔt equals the change in momentum; total momentum is conserved when net external impulse is zero, and kinetic energy is also conserved only in elastic collisions.

Circular motion: a_c = v²/r points toward the center; in an inertial frame there is no outward force, only real forces that supply the centripetal requirement.

Rotation: τ = rF sinθ, τ_net = Iα, L = Iω; angular momentum is conserved when net external torque is zero, so a skater pulling in the arms spins faster.

T(K) = T(°C) + 273.15 and T(°F) = 1.8·T(°C) + 32; gas and efficiency formulas require absolute (kelvin) temperature.

Linear expansion ΔL = αL₀ΔT; for an isotropic solid, area expansion uses about 2α and volume expansion about 3α.

Q = mcΔT applies to a temperature change; Q = mL applies to a phase change, during which the temperature stays constant even as energy is added or removed.

First law ΔU = Q − W with W the work done by the system; ΔU depends only on the end states, while Q and W depend on the path taken.

Second law: the entropy of an isolated system never decreases, heat moves spontaneously from hot to cold, and no engine between two reservoirs exceeds Carnot η = 1 − T_c/T_h.

Ideal gas PV = nRT = NkT, with R = 8.314 J/(mol·K) and k = 1.38×10⁻²³ J/K; at fixed temperature P₁V₁ = P₂V₂.

Kinetic theory: mean translational kinetic energy per molecule = (3/2)kT, so absolute temperature measures average molecular kinetic energy regardless of gas identity.

v_rms = √(3RT/M) = √(3kT/m); at the same temperature lighter molecules move faster, which is why hydrogen effuses more rapidly than oxygen.

Heat transfer modes: conduction Q/t = kAΔT/L by contact, convection by bulk fluid motion, and radiation by Stefan-Boltzmann P = σeAT⁴, which needs no medium.

For every wave v = fλ; the medium fixes the speed, the source fixes the frequency, and the wavelength adjusts when a wave enters a new medium.

Sound is a longitudinal pressure wave that needs a medium, travelling about 343 m/s in air at 20 °C, faster in solids, and not at all through a vacuum.

Superposition: a path difference of nλ gives constructive interference; a path difference of (n + ½)λ gives destructive interference.

Standing waves on a string fixed at both ends: f_n = nv/(2L); a pipe open at both ends matches this set, while a pipe closed at one end supports only odd harmonics f_n = nv/(4L).

Doppler shift f′ = f(v ± v_o)/(v ∓ v_s); observed frequency rises when source and observer approach and drops when they separate.

Reflection obeys θ_i = θ_r; refraction obeys Snell's law n₁sinθ₁ = n₂sinθ₂ with n = c/v, so light entering a denser medium slows and bends toward the normal.

Total internal reflection needs travel from higher to lower index with θ_i > θ_c, where sinθ_c = n₂/n₁; it is the principle behind optical fibers.

Thin lens and mirror equation 1/f = 1/d_o + 1/d_i with m = −d_i/d_o; real images are inverted, virtual images upright, and a diverging lens has f < 0.

Young's double slit gives bright fringes at d sinθ = mλ; a single slit gives dark fringes at a sinθ = mλ; diffraction reveals the wave nature of light while the photoelectric effect reveals the particle nature.

Coulomb's law F = k|q₁q₂|/r² with k = 8.99×10⁹ N·m²/C²; doubling either charge doubles the force, while doubling the separation quarters it.

Electric field E = F/q = kQ/r² points away from positive charge and toward negative charge; field lines never cross and their density indicates field strength.

Potential V = kQ/r and PE = qV; inside a uniform field E = V/d, and equipotential surfaces are always perpendicular to field lines.

Capacitors: C = Q/V, parallel plates C = ε₀A/d, stored energy U = ½CV²; parallel connection adds capacitance while series connection adds reciprocals.

Ohm's law V = IR with R = ρL/A; metals increase resistance as temperature rises, while many semiconductors decrease.

Series circuits share one current with R_eq = ΣR; parallel circuits share one voltage with 1/R_eq = Σ1/Rᵢ; power anywhere is P = IV = I²R = V²/R.

Kirchhoff's rules: currents entering a junction equal currents leaving (charge conservation), and the potential changes around any closed loop sum to zero (energy conservation).

Magnetic force F = qvB sinθ or F = ILB sinθ is perpendicular to both velocity and field, so it changes direction but does no work and cannot change speed.

Straight wire B = μ₀I/(2πr) and solenoid B = μ₀nI; Faraday's law ε = −NΔΦ/Δt with Lenz's law giving the induced current direction that opposes the flux change.

Photon energy E = hf = hc/λ with h = 6.63×10⁻³⁴ J·s; intensity sets the number of photons while frequency sets the energy of each one.

Photoelectric effect: K_max = hf − φ, and no electrons are emitted below the threshold frequency f₀ = φ/h no matter how intense the light.

de Broglie relation λ = h/p; electrons diffract like waves, and standing-wave conditions on the electron wave explain quantized atomic energy levels.

Hydrogen levels E_n = −13.6 eV/n²; a transition emits or absorbs a photon of energy |E_f − E_i|, producing line spectra, and ionizing from n = 1 requires 13.6 eV.

Heisenberg uncertainty ΔxΔp ≥ ħ/2 (and ΔEΔt ≥ ħ/2) is a limit on simultaneous knowledge of conjugate quantities, not a flaw in instruments.

Radioactive decays conserve mass number and charge: alpha emits a ⁴₂He nucleus, beta-minus turns a neutron into a proton plus electron and antineutrino, gamma is a photon from an excited nucleus.

N = N₀(1/2)^(t/T½); after n half-lives the fraction remaining is 2⁻ⁿ, and activity A = λN decays at the same exponential rate.

E = mc²; nuclear mass defect becomes binding energy using 1 u = 931.5 MeV, which is why fusing light nuclei and fissioning heavy ones both release energy.

Special relativity: light speed is the same for all inertial observers, moving clocks run slow by γ, lengths contract along the motion, and γ = 1/√(1 − v²/c²) grows without limit as v approaches c.