NSSCAS Physics (8225) cheat sheet

Average velocity = displacement / time; average speed = distance / time. Both are scalars except velocity, which is a vector.

Equations for uniform acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t.

Projectile motion: horizontal component of velocity is constant (if air resistance negligible); vertical acceleration is g downward.

For projectile launched at speed u and angle θ: time of flight = 2u sinθ / g (to same level); range = u² sin2θ / g.

Displacement–time graph gradient = velocity; velocity–time graph gradient = acceleration; area under velocity–time graph = displacement.

Relative velocity: v_AB = v_A − v_B (vector subtraction).

Angular velocity ω = 2π/T = 2πf; linear speed v = rω for circular motion.

Centripetal acceleration a = v²/r = rω² directed toward centre; centripetal force F = mv²/r.

Newton's first law: a body remains at rest or in uniform motion unless acted on by a resultant force.

Newton's second law: resultant force F = ma (or F = dp/dt).

Newton's third law: if A exerts a force on B, B exerts an equal and opposite force on A; forces act on different bodies.

Momentum p = mv (vector). Impulse = change in momentum = FΔt (area under force–time graph).

Conservation of linear momentum: total momentum of an isolated system remains constant.

Friction: limiting static friction F_max = μ_s N; kinetic friction F_k = μ_k N.

Moments: moment = force × perpendicular distance from pivot; principle of moments for equilibrium: sum of clockwise moments = sum of anticlockwise moments.

Centre of gravity: point where weight of body may be considered to act; for uniform regular shapes it is at the geometric centre.

Work done by a constant force: W = Fs cosθ, where θ is angle between force and displacement.

Kinetic energy KE = ½mv²; gravitational potential energy change ΔPE = mgΔh (near Earth's surface).

Elastic potential energy stored in a spring = ½kx² (or area under force–extension graph).

Work–energy theorem: net work done on an object equals its change in kinetic energy.

Conservation of energy: energy cannot be created or destroyed, only transferred between forms; total energy in a closed system is constant.

Power P = work done / time = energy transferred / time; average power P = Fv for constant force.

Efficiency = useful energy output / total energy input × 100% (or useful power output / total power input × 100%).

Density ρ = m/V; relative density = density of substance / density of water.

Hooke's law: extension is directly proportional to applied force up to the limit of proportionality: F = kx.

Stress = force / cross-sectional area (σ = F/A); strain = extension / original length (ε = x/L).

Young modulus E = stress / strain = (F/A) / (x/L) = FL/(Ax) for a wire.

Elastic deformation: material returns to original shape when force removed; plastic deformation: permanent change.

Ultimate tensile strength is the maximum stress a material can withstand before breaking.

Pressure in a fluid: p = F/A; pressure at depth h in a fluid of density ρ: p = p₀ + ρgh.

Archimedes' principle: upthrust on a body in a fluid equals the weight of fluid displaced.

Wave equation: v = fλ, where v is wave speed, f frequency, λ wavelength.

Transverse waves: oscillations perpendicular to direction of energy transfer (e.g., light). Longitudinal waves: oscillations parallel to direction of energy transfer (e.g., sound).

Refraction: n₁ sinθ₁ = n₂ sinθ₂ (Snell's law); refractive index n = c/v = sin i / sin r for light entering medium from vacuum/air.

Total internal reflection occurs when light travels from denser to less dense medium and angle of incidence exceeds critical angle C, where sin C = n₂/n₁.

Diffraction: spreading of waves when they pass through a gap or around an obstacle; significant when gap width ≈ wavelength.

Two-source interference: constructive interference when path difference = nλ; destructive when path difference = (n + ½)λ.

For double-slit interference: fringe spacing Δy = λD/d, where D is slit-to-screen distance and d is slit separation.

Sound intensity level β = 10 log₁₀(I/I₀) dB, with I₀ = 1 × 10⁻¹² W m⁻².

Electric current I = ΔQ/Δt; conventional current direction is opposite to electron flow.

Ohm's law: V = IR for a conductor at constant temperature; resistance R = V/I.

Resistivity ρ: R = ρL/A; resistance increases with length and decreases with cross-sectional area.

Resistors in series: R_total = R₁ + R₂ + …; in parallel: 1/R_total = 1/R₁ + 1/R₂ + …

Electrical power P = VI = I²R = V²/R.

Kirchhoff's laws: junction rule (sum of currents entering = sum leaving); loop rule (sum of e.m.f.s = sum of p.d.s around any closed loop).

E.m.f. ε and internal resistance r: terminal p.d. V = ε − Ir; power output = Iε − I²r.

Potential divider: V_out = V_in × R₂/(R₁ + R₂) for two resistors in series.

Gravitational field strength g = F/m; for a point mass g = GM/r²; gravitational potential energy U = −GMm/r.

Newton's law of gravitation: F = Gm₁m₂/r².

Electric field strength E = F/q; for a point charge E = kQ/r² (k = 1/(4πε₀)); electric potential V = kQ/r.

Coulomb's law: F = kQ₁Q₂/r².

Magnetic flux density B: force on current-carrying conductor F = BIL sinθ; force on moving charge F = Bqv sinθ.

Magnetic flux Φ = BA cosθ; Faraday's law: induced e.m.f. ε = −dΦ/dt; Lenz's law: induced current opposes change in flux.

Transformer equation: V_s/V_p = N_s/N_p (ideal transformer); power input = power output for ideal transformer.

Motion of charged particle in uniform magnetic field: circular path with radius r = mv/(Bq).

Temperature is a measure of average kinetic energy of particles; absolute zero = −273.15 °C = 0 K.

Specific heat capacity c: energy Q = mcΔT.

Specific latent heat L: energy Q = mL (for change of state at constant temperature).

Ideal gas equation: pV = nRT, where R = 8.31 J mol⁻¹ K⁻¹; also pV = NkT with k = 1.38 × 10⁻²³ J K⁻¹.

Kinetic theory: average kinetic energy of gas molecules = (3/2)kT; root-mean-square speed v_rms = √(3kT/m) = √(3RT/M).

First law of thermodynamics: ΔU = Q − W, where Q is heat added to system and W is work done by system.

Thermal conduction: rate of heat transfer P = kAΔT/L (k = thermal conductivity).

Boyle's law: p ∝ 1/V at constant T; Charles's law: V ∝ T at constant p; pressure law: p ∝ T at constant V.

Precision: closeness of repeated measurements to each other; accuracy: closeness to true value.

Random errors affect precision and can be reduced by repeating measurements and averaging; systematic errors affect accuracy and cannot be reduced by averaging.

Uncertainty: for a single reading, use ± half the smallest division; for digital instruments, ± the last digit.

Combining uncertainties: for addition/subtraction, add absolute uncertainties; for multiplication/division, add percentage uncertainties.

Percentage uncertainty = (absolute uncertainty / measured value) × 100%.

Graph plotting: plot independent variable on x-axis and dependent variable on y-axis; draw line of best fit; gradient = Δy/Δx.

Determining uncertainty in gradient: use maximum and minimum gradient lines from error bars or extreme points.

Significant figures: final answer should have same number of significant figures as the least precise measurement used in calculation.