MATSEC SEC Physics cheat sheet

Average speed = total distance ÷ total time; average velocity = displacement ÷ time, with direction.

Acceleration a = (v − u)/t; for uniform acceleration use v = u + at, s = ut + ½at², v² = u² + 2as.

On a distance–time graph, gradient = speed; on a velocity–time graph, gradient = acceleration and area under the line = displacement.

Newton's second law: resultant force F = ma, with F in newtons, m in kilograms, a in m/s².

Weight W = mg, where g ≈ 9.8 N/kg (often taken as 10 N/kg); mass is in kg and does not change with location.

Friction and air resistance oppose relative motion; terminal velocity is reached when drag equals weight so resultant force is zero.

Momentum p = mv is conserved in collisions and explosions when no external resultant force acts; impulse Ft = change in momentum.

A body is in equilibrium when the resultant force is zero and the sum of clockwise moments equals the sum of anticlockwise moments about any point.

Work done W = Fd, where F is the component of force along the displacement; unit joule (J).

Kinetic energy KE = ½mv²; gravitational potential energy change ΔPE = mgΔh.

Conservation of energy: energy is transferred between stores but never created or destroyed; lost mechanical energy usually becomes thermal energy.

Power P = W/t = E/t, measured in watts (W); 1 W = 1 J/s.

Efficiency = useful output energy ÷ total input energy × 100%, always less than 100% in real machines.

Energy resources are renewable (solar, wind, hydro, tidal, geothermal, biomass) or non-renewable (coal, oil, gas, nuclear fuel).

Sankey diagrams show input energy width and branch widths proportional to energy transferred, with wasted energy shown downwards.

Wave equation v = fλ; frequency f in hertz, wavelength λ in metres, speed v in m/s.

Transverse waves oscillate perpendicular to energy transfer (light, water waves); longitudinal waves oscillate parallel (sound).

Frequency is set by the source and stays constant when a wave crosses a boundary; speed and wavelength change on refraction.

Law of reflection: angle of incidence equals angle of reflection, both measured from the normal.

Refraction towards the normal occurs when light enters a denser medium (higher refractive index); Snell's law n₁sin θ₁ = n₂sin θ₂.

Sound needs a medium, travels fastest in solids and slowest in gases, and cannot travel through a vacuum.

The law of reflection and ray diagrams apply to plane mirrors; images in a plane mirror are virtual, laterally inverted and the same size.

Converging lenses focus parallel rays at the principal focus; a real image is formed when the object is beyond the focal length.

Temperature is a measure of average kinetic energy of particles; thermal energy transfer occurs from hot to cold regions.

Specific heat capacity: E = mcΔθ, where c is energy needed to raise 1 kg by 1 °C (water c ≈ 4200 J/kg °C).

Specific latent heat: E = mL, energy to change state at constant temperature without changing temperature.

Conduction transfers energy by particle collisions and free electrons, mainly in solids; convection occurs in fluids by density changes.

Thermal radiation is infrared and needs no medium; dark, matt surfaces absorb and emit better than shiny, light surfaces.

Boyle's law for a fixed mass of gas at constant temperature: p₁V₁ = p₂V₂.

Pressure law at constant volume: p₁/T₁ = p₂/T₂, with T in kelvin; Kelvin = Celsius + 273.

Thermal expansion occurs because particles vibrate more and occupy slightly more space as temperature rises.

Current I = Q/t, measured in amperes; conventional current flows from positive to negative.

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistance R = V/I in ohms.

Series circuits: same current everywhere; total resistance R = R₁ + R₂ + …; supply voltage divides between components.

Parallel circuits: same voltage across each branch; total current is the sum of branch currents; total resistance is less than the smallest branch resistance.

Electrical power P = VI = I²R = V²/R; energy transferred E = Pt, with domestic energy often in kilowatt-hours.

A fuse or circuit breaker protects a circuit by melting or tripping when current exceeds a safe value.

Magnetic field lines run from north to south outside a magnet; a current-carrying wire in a magnetic field experiences a force (motor effect).

Electromagnetic induction: a changing magnetic flux through a conductor induces an emf; the induced current opposes the change (Lenz's law).

Density ρ = m/V, in kg/m³; a body floats when its average density is less than the fluid's density.

Pressure p = F/A, in pascals (Pa); 1 Pa = 1 N/m².

Pressure in a liquid p = ρgh, depending on depth, density and g, not on the shape of the container.

Atmospheric pressure decreases with height and is measured with a barometer; a manometer measures gas pressure differences.

Pascal's principle: pressure applied to an enclosed fluid is transmitted equally in all directions (hydraulic systems).

Upthrust equals the weight of fluid displaced (Archimedes' principle); apparent weight = true weight − upthrust.

Particle model of matter: solids have fixed particle positions, liquids are close but mobile, gases are widely spaced and move randomly.

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

A measuring instrument's resolution is the smallest change it can detect; read to half the smallest division where appropriate.

Random errors scatter readings about a mean and are reduced by repeating; systematic errors shift all readings the same way and are reduced by calibration.

Precision describes consistency of repeated readings; accuracy describes closeness to the true value.

For a set of readings, mean = sum of readings ÷ number of readings; discard obvious anomalies and state why.

When plotting graphs, plot the independent variable on the x-axis and label axes with quantity, symbol and unit.

A straight-line graph through the origin shows direct proportionality; gradient units come from the y-axis unit divided by the x-axis unit.

Control variables are kept constant to make a fair test; the independent variable is changed and the dependent variable is measured.

Safety precautions in physics practicals include checking apparatus for damage, using low voltages, and keeping liquids away from electrical equipment.