BGCSE Physics 1427 cheat sheet

Constant-acceleration equations: v = u + at, s = ut + ½at², v² = u² + 2as; these apply only when acceleration is uniform and motion is in a straight line.

Newton's second law: resultant force F = ma, with F in newtons, m in kilograms and a in m/s²; a resultant force of zero means velocity is constant or zero.

Mass is a scalar measured in kilograms and does not change with location; weight is a force W = mg, with g ≈ 9.8 N/kg near the Earth's surface.

Moment of a force = force × perpendicular distance from the pivot to the line of action, measured in N m; principle of moments: in equilibrium, total clockwise moment about a point = total anticlockwise moment about the same point.

Work done W = Fd only when the force acts along the displacement; power P = W/t = Fv; one watt is one joule per second.

Kinetic energy = ½mv², gravitational potential energy = mgh; energy is conserved overall but friction and air resistance dissipate it as thermal energy.

Machine quantities: mechanical advantage = load/effort, velocity ratio = distance moved by effort/distance moved by load, efficiency = (useful output energy/total input energy) × 100% = (MA/VR) × 100%.

Momentum p = mv is conserved in any collision where no external resultant force acts; impulse Ft equals the change in momentum.

Hooke's law: extension is proportional to applied force (F = kx) up to the limit of proportionality, where k is the spring constant in N/m.

Current I = Q/t is the rate of flow of charge; one ampere is one coulomb per second, and conventional current runs from positive to negative outside the source.

Ohm's law V = IR applies to metallic conductors at constant temperature; resistance R = V/I is measured in ohms, where 1 Ω carries 1 A under 1 V.

Series circuits: the current is identical everywhere, the supply p.d. is shared between components, and R_total = R₁ + R₂ + … .

Parallel circuits: the p.d. across each branch is the same, the supply current is the sum of branch currents, and 1/R_total = 1/R₁ + 1/R₂ + … .

Electrical power P = VI = I²R = V²/R; energy transferred E = Pt, and one kilowatt-hour equals 3.6 × 10⁶ J.

EMF is the energy transferred per coulomb from the source; potential difference is the energy transferred per coulomb from the charge to a component.

Resistance of a wire increases with length and temperature and decreases with cross-sectional area: R = ρL/A, where ρ is the resistivity of the material.

A current-carrying conductor in a magnetic field experiences a force F = BIL sin θ, with direction given by Fleming's left-hand rule; a changing magnetic flux linkage induces an emf (Faraday's law) whose direction opposes the change (Lenz's law).

A fuse is connected in the live wire and melts when current exceeds its rating; the earth wire gives a low-resistance path so a faulty case cannot stay live.

Wave equation v = fλ: speed in m/s equals frequency in Hz multiplied by wavelength in m; frequency is set by the source and speed by the medium.

Transverse waves (light, water ripples) oscillate perpendicular to the direction of energy transfer; longitudinal waves (sound) oscillate parallel to it and need a medium.

Law of reflection: angle of incidence = angle of reflection, both measured from the normal; a plane mirror forms a virtual, upright, laterally inverted image of the same size, as far behind the mirror as the object is in front.

Refraction occurs because wave speed changes between media; light entering a denser medium slows and bends towards the normal, and Snell's law gives n₁ sin θ₁ = n₂ sin θ₂, with n = c/v.

Total internal reflection happens only when light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle c, where sin c = 1/n.

A convex (converging) lens has focal length f and power P = 1/f in dioptres; parallel rays converge at the principal focus, and an object closer than f produces a virtual, magnified, upright image.

Lens and mirror equation 1/f = 1/u + 1/v, with magnification m = v/u = image height/object height; real images are inverted and can be projected on a screen.

Sound is a longitudinal wave requiring a medium; in air at room temperature it travels at about 340 m/s, and frequency determines pitch while amplitude determines loudness.

Diffraction is the spreading of waves at gaps or around obstacles; it is most noticeable when the gap width is comparable to the wavelength, and larger wavelengths diffract more.

Temperature measures the average kinetic energy of particles and is measured in °C or K (T/K = θ/°C + 273); heat is energy transferred because of a temperature difference.

Conduction transfers energy through a material by vibrating particles and free electrons without bulk movement; metals conduct well because of their free electrons.

Convection transfers energy by the bulk movement of a fluid: heated fluid expands, becomes less dense and rises, while cooler fluid sinks; it cannot occur in solids.

Thermal radiation is infrared electromagnetic radiation emitted by any body above absolute zero; it needs no medium, and dark matt surfaces absorb and emit better than shiny light ones.

Linear expansion ΔL = αL₀ΔT; expansion gaps are left in rails and bridges, and a bimetallic strip bends because its two metals expand by different amounts.

Specific heat capacity: Q = mcΔT, where c for water is about 4200 J/(kg °C); the large value makes water a good coolant and storage heater medium.

Specific latent heat: Q = mL for melting/boiling or condensing/freezing; temperature stays constant during a change of state because energy goes into breaking or forming bonds.

For a fixed mass of ideal gas, pV/T = constant with T in kelvin; at constant temperature p₁V₁ = p₂V₂, and at constant volume p/T is constant.

A thermometer is calibrated at the ice point (0 °C) and steam point (100 °C) at standard atmospheric pressure, with the scale divided into equal intervals.

An atom has a small, dense nucleus of protons (charge +1, mass about 1 u) and neutrons (no charge), surrounded by electrons in shells; the nucleus holds nearly all the mass.

Proton number Z fixes the element; nucleon number A = Z + N, and nuclides are written ᴬ_Z X; isotopes have the same Z but different N.

Alpha decay emits a helium nucleus (⁴₂He): A falls by 4 and Z falls by 2. Beta decay converts a neutron to a proton, so Z rises by 1 and A is unchanged. Gamma emission changes neither A nor Z.

Penetration: alpha is stopped by paper or a few centimetres of air, beta by a few millimetres of aluminium, gamma is reduced only by thick lead or concrete; ionising power is in the reverse order.

Half-life is the time for half the unstable nuclei in a sample to decay, or for its activity to halve; after n half-lives the remaining fraction is (1/2)ⁿ.

Activity is measured in becquerels (one decay per second); decay is random, so half-life predictions are statistical and exact times for individual nuclei cannot be given.

Background radiation comes from cosmic rays, rocks and radon gas, and medical or industrial sources; it must be measured and subtracted in school experiments.

Uses include gamma sterilising of equipment, gamma and beta sources for cancer treatment, beta thickness gauges, and radioactive tracers in medicine and industry.

Safety with sources relies on maximum distance, minimum exposure time, lead or concrete shielding, and handling with tongs while storing sources in labelled lead containers.

SI base units: metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount of substance) and candela (luminous intensity).

Prefix conversions: k = 10³, c = 10⁻², m = 10⁻³, μ = 10⁻⁶, n = 10⁻⁹; convert all readings to SI units before substituting into a formula.

Read an analogue scale to the smallest division plus one estimated digit, and always quote the unit; the reading uncertainty is at least half the smallest division.

Precision means repeated readings agree closely; accuracy means the reading is close to the true value. Random errors scatter readings and are reduced by averaging repeats; systematic errors shift all readings the same way, as with a zero error.

Vernier callipers measure external, internal and depth dimensions to about 0.1 mm: read the main scale at the vernier zero, then add the vernier division that aligns with a main-scale mark.

A micrometer screw gauge reads to 0.01 mm; check the zero reading with the jaws closed and subtract any zero error from all measurements.

Uncertainties combine by rule: for addition or subtraction add the absolute uncertainties; for multiplication or division add the percentage uncertainties.

Data handling: take the mean of repeats, identify and exclude anomalous points, plot the independent variable on the x-axis, draw a line of best fit, and find the gradient as Δy/Δx.

Density ρ = m/V; measure a regular solid with a rule and callipers and an irregular solid by displacement in a measuring cylinder, avoiding parallax by reading at eye level.