Every Physics concept in the high school Science Bowl study set (grades 9-12), with a short definition for each. Read through them here, then drill them as flashcards or practise real Physics questions.
1st (Inertia): object stays at rest or in uniform motion without net force. 2nd: F = ma — net force equals mass × acceleration. 3rd: every action has an equal and opposite reaction. Weight W = mg (g ≈ 9.8 m/s²). Normal force is perpendicular to a surface.
Equations (constant acceleration): v = v₀ + at; x = v₀t + ½at²; v² = v₀² + 2ax. Free fall: a = g = 9.8 m/s² downward. Projectile motion: horizontal velocity is constant; vertical component experiences g independently.
Work W = Fd·cosθ (Joules). Kinetic energy KE = ½mv². Gravitational PE = mgh. Work-energy theorem: net work = ΔKE. Conservation of mechanical energy (no friction): KE + PE = constant. Power P = W/t = Fv (Watts). 1 hp = 746 W.
Momentum p = mv (kg·m/s). Impulse J = FΔt = Δp. Conservation of momentum: total momentum conserved in closed system. Elastic collision: KE conserved. Inelastic: KE not conserved. Perfectly inelastic: objects stick together.
Transverse: displacement perpendicular to propagation (light, EM). Longitudinal: displacement parallel (sound). Wave speed v = fλ. Amplitude: maximum displacement. Constructive interference: in phase. Destructive: out of phase. Standing waves: nodes (zero displacement) and antinodes (max displacement).
Increasing frequency (decreasing λ): Radio → Microwave → Infrared → Visible (ROY G BIV) → UV → X-ray → Gamma. All travel at c = 3×10⁸ m/s in a vacuum. Photon energy E = hf. Higher frequency = more energy = more ionizing radiation.
Ohm's Law: V = IR. Series: same current, voltages add, R_total = ΣRᵢ. Parallel: same voltage, currents add, 1/R_total = Σ(1/Rᵢ). Power P = IV = I²R = V²/R. Kirchhoff's junction rule: currents in = currents out. Loop rule: sum of voltages around a closed loop = 0.
0th Law: thermal equilibrium is transitive. 1st Law: ΔU = Q − W. 2nd Law: entropy of isolated system never decreases; heat flows from hot to cold. 3rd Law: entropy → 0 as T → 0 K. Carnot efficiency (maximum): η = 1 − Tc/Th.
Magnetic force on charge: F = qv×B. Right-hand rule for current direction and field. Faraday's Law: ε = −ΔΦ/Δt (changing flux induces EMF). Lenz's Law: induced current opposes flux change. Transformer: Vp/Vs = Np/Ns. AC generation via rotating coils in magnetic fields.
Photoelectric effect (Einstein): E = hf − work function; proved light's particle nature. de Broglie: matter wavelength λ = h/p. Heisenberg uncertainty: Δx·Δp ≥ ℏ/2. Special relativity: E = mc²; time dilation t' = t/√(1−v²/c²); length contraction. Nuclear binding energy from mass defect.
Centripetal acceleration: aₓ = v²/r (directed toward center). Centripetal force: Fc = mv²/r. Newton's Law of Universal Gravitation: F = Gm₁m₂/r². Kepler's Laws: 1st (elliptical orbits), 2nd (equal areas in equal times), 3rd (T² ∝ r³ — orbital period vs semi-major axis).
Oscillation where restoring force ∝ displacement (F = −kx). Period of spring: T = 2π√(m/k). Period of pendulum: T = 2π√(L/g) — independent of amplitude (for small angles). At equilibrium: max velocity, zero PE stored. At extremes: zero velocity, max PE. Total energy E = ½kA² (constant).
Pressure P = F/A; in a fluid P = ρgh. Archimedes' Principle: buoyant force = weight of displaced fluid. Pascal's Law: pressure applied to enclosed fluid transmits equally. Bernoulli's Equation: P + ½ρv² + ρgh = constant (faster flow → lower pressure). Continuity: A₁v₁ = A₂v₂.
Law of reflection: angle of incidence = angle of reflection. Snell's Law (refraction): n₁sinθ₁ = n₂sinθ₂. Total internal reflection: when angle exceeds critical angle (n₁ > n₂). Lenses: converging (convex) focuses light; diverging (concave) spreads light. Mirror equation: 1/f = 1/dₒ + 1/dᵢ.
Longitudinal mechanical wave; requires medium. Speed in air ≈ 343 m/s (20°C). Intensity measured in decibels (dB): logarithmic scale, 10 dB increase = 10× intensity. Doppler effect: source moving toward observer → higher frequency (pitch). Standing waves in pipes/strings produce harmonics.
Coulomb's Law: F = kq₁q₂/r² (k = 9×10⁹ N·m²/C²). Electric field E = F/q = kq/r² (points away from + charges, toward − charges). Electric potential energy U = kq₁q₂/r. Electric potential V = kq/r (volts). Work done moving charge: W = qΔV. Field lines perpendicular to equipotential surfaces.
Angular velocity ω = Δθ/Δt (rad/s). Torque τ = rF·sinθ (N·m). Moment of inertia I: resistance to angular acceleration. Newton's 2nd Law for rotation: τ = Iα. Angular momentum L = Iω; conserved when net torque = 0 (explains spinning figure skater). Rolling without slipping: v = rω.
Nucleus held together by strong nuclear force (overcomes Coulomb repulsion). Binding energy: energy released when nucleons combine (mass defect × c²). Iron-56 has highest binding energy per nucleon. Radioactive decay: alpha (A−4, Z−2), beta-minus (Z+1), beta-plus (Z−1), gamma (no change in A or Z).
Store electrical energy in an electric field between two conducting plates. Capacitance C = Q/V (Farads). Energy stored: U = ½CV² = Q²/2C. Parallel plate capacitor: C = ε₀A/d. Adding a dielectric increases capacitance. Series: 1/C_total = Σ(1/Cᵢ). Parallel: C_total = ΣCᵢ.
Checking and converting units using known equivalences. SI base units: meter (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount), candela (luminous intensity). Derived units: Newton = kg·m/s², Joule = N·m = kg·m²/s², Pascal = N/m², Watt = J/s.
Force per unit area: P = F/A (Pascals). Atmospheric pressure at sea level ≈ 101,325 Pa = 1 atm = 760 mmHg = 760 torr. Gauge pressure = absolute pressure − atmospheric pressure. Vacuum gauge reads relative to atmosphere. Manometers and barometers measure pressure differences.
Apparent change in frequency due to relative motion between source and observer. Source moving toward observer: higher observed frequency. Source moving away: lower frequency. f_obs = f_source × (v ± v_obs)/(v ∓ v_source). Applies to sound and light; redshift (galaxies moving away) is the Doppler effect for light.
Electrical power P = IV = I²R = V²/R (Watts). Energy E = Pt (Joules or kWh). Transformers change voltage for efficient long-distance transmission (high V, low I reduces resistive losses P = I²R). AC voltage is described by RMS values: V_rms = V_peak/√2.
Light exhibits wave-particle duality. As a wave: interference, diffraction, polarization. As a particle (photon): energy E = hf = hc/λ. Photoelectric effect confirms particle nature. Double-slit experiment demonstrates wave nature. Photons carry momentum p = h/λ. Speed of light c = 3×10⁸ m/s in vacuum.
Einstein's postulates: laws of physics same in all inertial frames; speed of light c is constant for all observers. Consequences: time dilation (moving clocks run slow), length contraction (moving objects shorter in direction of motion), mass-energy equivalence E = mc². Nothing with mass can reach c.
Gravitational field strength g = GM/r² (N/kg or m/s²). Near Earth's surface, g ≈ 9.8 m/s². Gravitational potential energy: U = −GMm/r (negative, bound system). Escape velocity: v_esc = √(2GM/r). Orbital velocity: v_orb = √(GM/r). Black holes have escape velocity ≥ c.
Static friction: force preventing stationary objects from sliding; fₛ ≤ μₛN. Kinetic friction: force opposing sliding motion; fₖ = μₖN. Rolling friction: much less than sliding. μₛ > μₖ (harder to start motion than sustain it). Normal force N: perpendicular contact force. On inclined plane: N = mg·cosθ; friction force = μmg·cosθ; net force along plane = mg·sinθ − μmg·cosθ. Air resistance is a velocity-dependent drag force.
Two-dimensional motion under gravity; horizontal and vertical components are independent. Horizontal: uniform motion, vₓ = v₀cosθ, x = v₀cosθ · t. Vertical: uniform acceleration, vᵧ = v₀sinθ − gt, y = v₀sinθ · t − ½gt². Range R = v₀²sin(2θ)/g (maximum at 45°). At maximum height: vᵧ = 0. Time of flight: t = 2v₀sinθ/g. Neglects air resistance.
Torque τ = r × F = rF sinθ (N·m); the rotational equivalent of force. For static equilibrium: ΣF = 0 (translational) AND Στ = 0 (rotational). Torque is positive (counterclockwise) or negative (clockwise) about a chosen pivot. Lever arm: perpendicular distance from pivot to line of action of force. Center of mass: point where gravity effectively acts. A uniform rod's center of mass is at its midpoint.
Temperature measures average kinetic energy of particles (K = −273.15°C). Heat Q = mcΔT where c = specific heat capacity (J/kg·K). Water: c = 4186 J/kg·K (highest of common substances — moderates climate). Latent heat: Q = mL; energy for phase change at constant temperature. Lf (fusion) for water = 334 kJ/kg; Lv (vaporization) = 2260 kJ/kg. Calorimetry: heat lost by hot object = heat gained by cold (Q_lost = Q_gained).
Diffraction: bending of waves around obstacles or through slits; significant when slit width ≈ wavelength. Single-slit diffraction: minima at a sinθ = mλ. Double-slit (Young's experiment): constructive interference at d sinθ = mλ; bright fringes spaced Δy = λL/d. Thin film interference: path difference = 2t; phase shift on reflection from denser medium. Diffraction gratings: d sinθ = mλ; bright spots at each order m.
Magnetic flux Φ = BA cosθ (Weber). Faraday's Law: induced EMF ε = −ΔΦ/Δt (rate of flux change). Lenz's Law: induced current opposes the change that caused it (−sign). EMF can be induced by: changing B, changing area, or changing angle. Motional EMF: ε = BLv (conductor of length L moving at speed v through field B). Generators: rotating loop in B field produces sinusoidal AC. Transformers: Vp/Vs = Np/Ns; IpNp = IsNs.
Standing wave: superposition of two identical waves traveling in opposite directions; produces nodes (zero displacement) and antinodes (max displacement). String (fixed both ends): fundamental f₁ = v/2L; harmonics fₙ = nv/2L. Open pipe (open both ends): same as string. Closed pipe (one end closed): only odd harmonics; f₁ = v/4L; fₙ = nv/4L (n = 1, 3, 5…). Resonance: driving frequency matches natural frequency → maximum amplitude.
RC circuit (resistor + capacitor): charging — V_C = V₀(1 − e^(−t/RC)); discharging — V_C = V₀e^(−t/RC). Time constant τ = RC; after one τ, capacitor charges to ~63% of final voltage. Impedance in AC circuits: capacitive reactance Xc = 1/(2πfC); inductive reactance XL = 2πfL. At resonance in LC circuit: f = 1/(2π√(LC)). Phase relationships: current leads voltage in capacitor; lags in inductor.
Bohr model (1913): electrons orbit nucleus at fixed radii; energy quantized. Energy levels: Eₙ = −13.6 eV/n² for hydrogen. Electron absorbs photon → jumps to higher level (absorption spectrum). Electron falls to lower level → emits photon of energy E = hf = ΔE (emission spectrum). Lyman series: transitions to n=1 (UV). Balmer series: to n=2 (visible). Paschen: to n=3 (IR). Rydberg equation: 1/λ = R(1/n₁² − 1/n₂²).
Standard Model: matter made of fermions (quarks + leptons). Quarks: up (u), down (d), charm (c), strange (s), top (t), bottom (b). Proton = uud; neutron = udd. Leptons: electron, muon, tau and their neutrinos. Forces carried by bosons: photon (electromagnetic), W/Z bosons (weak), gluons (strong), graviton (hypothetical, gravity). Antimatter: opposite charge/quantum numbers. Pair production: γ → e⁻ + e⁺.
Scalar: magnitude only (mass, speed, temperature, energy). Vector: magnitude + direction (velocity, force, acceleration, displacement, momentum). Vector addition: tip-to-tail or parallelogram method. Component method: break into x/y components, add separately. Resultant magnitude: R = √(Rₓ² + Rᵧ²); angle: θ = arctan(Rᵧ/Rₓ). Dot product (scalar): A·B = AB cosθ. Cross product (vector): A×B, magnitude AB sinθ, direction by right-hand rule.
Most materials expand when heated. Linear expansion: ΔL = αL₀ΔT (α = coefficient of linear expansion). Volume expansion: ΔV = βV₀ΔT; β ≈ 3α. Water anomaly: maximum density at 4°C; expands on freezing (ice less dense than liquid water — important for aquatic life). Bimetallic strips: two metals with different α bonded together; bend on heating (used in thermostats). Thermal stress: if expansion is constrained, large forces develop.
Archimedes' Principle: buoyant force = weight of fluid displaced (F_b = ρ_fluid · V_submerged · g). Object floats if F_b ≥ weight (density of object ≤ density of fluid). Fully submerged: F_b = ρ_fluid · V_object · g (independent of depth). Apparent weight = actual weight − F_b. Applications: ships (large volume displaces much water), submarines (change buoyancy by flooding/emptying ballast tanks), hot air balloons (less dense than cool air).
Angular momentum L = Iω; conserved when net external torque = 0. Moment of inertia I depends on mass distribution (I = mr² for point mass; I = ½mr² for solid disk; I = ⅔mr² for hollow sphere). Spinning figure skater: pulls arms in → I decreases → ω increases (L constant). Gyroscope: resists changes in orientation. Precession: gyroscope axis rotates due to gravity torque. Conservation of L explains planetary orbits (Kepler's 2nd Law — equal areas in equal times).