NSSCO Physics (6118) cheat sheet

SI base units: metre (m) length, kilogram (kg) mass, second (s) time, ampere (A) current, kelvin (K) temperature, mole (mol) amount of substance, candela (cd) luminous intensity.

Derived units: N = kg m s^-2; J = N m = kg m^2 s^-2; W = J s^-1; Pa = N m^-2; C = A s; V = J C^-1 = W A^-1; ohm = V A^-1.

Prefixes: nano 10^-9, micro 10^-6, milli 10^-3, centi 10^-2, kilo 10^3, mega 10^6, giga 10^9.

Density p = m/V in kg m^-3; regular solid volume from dimensions, irregular solid volume by displacement in a measuring cylinder.

Resolution of instruments: metre rule 1 mm, vernier calliper 0.1 mm, micrometer screw gauge 0.01 mm.

Reading uncertainty: analogue scale +/- half the smallest division; digital display +/- the last digit shown.

Random error is reduced by repeat readings and averaging; systematic error such as zero error shifts every reading the same way and must be subtracted, not averaged out.

Perpendicular vectors add by Pythagoras, magnitude sqrt(x^2 + y^2); non-perpendicular vectors add by scale drawing (nose-to-tail) or by resolving into components.

Constant-acceleration equations: v = u + at; s = ut + 0.5at^2; v^2 = u^2 + 2as; s = 0.5(u + v)t.

Gradient of a displacement-time graph = velocity; gradient of a velocity-time graph = acceleration; area under a velocity-time graph = displacement.

Newton's first law: a body stays at rest or moves with constant velocity in a straight line unless a resultant external force acts on it.

Newton's second law: resultant force F = ma (F in N, m in kg, a in m s^-2); weight W = mg with g about 9.8 N kg^-1 near the Earth's surface.

Newton's third law: if A exerts a force on B, B exerts an equal and opposite force on A; the two forces act on different bodies and never cancel on one object.

Momentum p = mv is a vector in kg m s^-1; total momentum is conserved in collisions and explosions when no external resultant force acts.

Impulse = Ft = change in momentum = mv - mu; the area under a force-time graph equals the impulse.

Friction and drag oppose relative motion; terminal velocity is reached when drag equals weight, so the resultant force and acceleration are zero.

Work W = Fd, where d is the distance moved along the direction of the force; 1 J = 1 N m.

Kinetic energy KE = 0.5mv^2; change in gravitational potential energy = mg(delta h).

Conservation of energy: energy is neither created nor destroyed, only transferred between stores; total energy in = total energy out.

Power P = W/t = E/t = Fv; 1 W = 1 J s^-1.

Efficiency = (useful energy output / total energy input) x 100%; friction, heating and sound always make efficiency less than 100%.

Pressure p = F/A in pascals (Pa = N m^-2); for the same force, a smaller contact area gives a larger pressure.

Pressure in a liquid p = rho g h; at a given depth it acts equally in all directions and does not depend on the shape or width of the container.

Pascal's principle: pressure applied to an enclosed fluid is transmitted undiminished, so F1/A1 = F2/A2 in a hydraulic system.

Upthrust equals the weight of fluid displaced (Archimedes' principle); a body floats when upthrust equals its weight and sinks when its weight is greater.

Temperature measures the average kinetic energy of particles; heat is energy in transit because of a temperature difference, so a body does not contain 'heat'.

Specific heat capacity c: Q = mc(delta theta); for water c is about 4200 J kg^-1 K^-1, so 4200 J raises 1 kg by 1 K.

Specific latent heat L: Q = mL, the energy to change state at constant temperature; for water the latent heat of vaporisation is about 2.26 x 10^6 J kg^-1.

Conduction in solids relies on particle vibration and free electrons; convection in fluids relies on density differences; radiation is infrared electromagnetic waves and needs no medium.

Dull black surfaces are good absorbers and emitters of infrared; shiny light surfaces are poor absorbers and good reflectors.

Gas laws for a fixed mass: Boyle p1V1 = p2V2 at constant T; pressure law p1/T1 = p2/T2 at constant V; Charles V1/T1 = V2/T2 at constant p; T must be in kelvin.

Kelvin temperature T = theta(degrees C) + 273; a temperature change of 1 K equals a change of 1 degree C.

Evaporation happens below the boiling point at the liquid surface; it speeds up with higher temperature, larger surface area, moving air and lower humidity, and it cools the remaining liquid.

A wave transfers energy without transferring matter; mechanical waves need a medium, electromagnetic waves travel through vacuum.

Transverse waves oscillate perpendicular to the direction of travel (light, water ripples); longitudinal waves oscillate parallel to travel, forming compressions and rarefactions (sound).

Wave quantities: amplitude = maximum displacement; wavelength lambda = crest to crest; frequency f = oscillations per second; period T = 1/f.

Wave equation v = f lambda; the speed in a given medium is fixed, so a higher frequency means a shorter wavelength.

At a boundary between media the frequency stays constant while speed and wavelength change, causing a change of direction (refraction).

Reflection: angle of incidence = angle of reflection. Diffraction: spreading of waves at a gap or edge. Interference: superposition of waves from two coherent sources.

Diffraction is greatest when the gap width is about equal to the wavelength, and is negligible when the gap is much wider.

Electromagnetic spectrum in order of increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays; all travel at 3.0 x 10^8 m s^-1 in vacuum.

Sound is a longitudinal wave that needs a medium; it travels at about 340 m s^-1 in air and faster in liquids and solids, but not through vacuum.

Audible range is about 20 Hz to 20 kHz; ultrasound is above 20 kHz and is used in sonar, medical imaging and cleaning.

Echo ranging: 2d = v t, so d = v t / 2, because the sound travels to the reflector and back.

Law of reflection: angle of incidence = angle of reflection, both measured from the normal; a plane mirror forms a virtual, upright, same-size, laterally inverted image.

Refraction: light bends towards the normal entering a denser medium (slower) and away from the normal entering a less dense medium (faster).

Refractive index n = sin i / sin r = speed in vacuum / speed in medium; the critical angle is given by sin c = 1/n.

Total internal reflection occurs for light travelling from a denser to a less dense medium when the angle of incidence exceeds the critical angle; used in optical fibres and prisms.

Converging lens: parallel rays meet at the principal focus, focal length f, power P = 1/f in dioptres (D). Real images are inverted and can be projected; virtual images are upright.

A prism disperses white light because the refractive index differs for each colour; red is deviated least and violet most.

Current I = Q/t is the rate of flow of charge, measured with an ammeter in series; conventional current flows from positive to negative.

Potential difference V = W/Q is energy transferred per unit charge, measured with a voltmeter in parallel across the component.

Ohm's law: V = IR for a metallic conductor at constant temperature; resistance R = V/I in ohms and equals the gradient of a V-I graph.

Series: current is the same everywhere, voltage splits, R = R1 + R2 + ... Parallel: voltage is the same, current splits, 1/R = 1/R1 + 1/R2 + ...

Power P = VI = I^2R = V^2/R; energy E = Pt, with domestic energy measured in kilowatt-hours (1 kWh = 3.6 x 10^6 J).

Magnetic field lines run from north to south outside a magnet and never cross; a current-carrying solenoid behaves like a bar magnet and an iron core makes an electromagnet.

Motor effect: a conductor carrying current at right angles to a magnetic field feels a force F = BIl; the direction is given by Fleming's left-hand rule.

Electromagnetic induction: relative motion between a magnet and a coil, or a changing magnetic field, induces a voltage whose direction opposes the change (Lenz's law).

Transformer: Vp/Vs = Np/Ns; for an ideal transformer VpIp = VsIs, so a step-up transformer raises voltage and lowers current.

The atom has a small, dense, positively charged nucleus of protons and neutrons, surrounded by electrons; most of the atom is empty space.

Proton number Z = number of protons, which fixes the element; nucleon number A = protons + neutrons; isotopes have the same Z but different A.

Alpha decay: an alpha particle is a helium nucleus (2 protons, 2 neutrons), so A falls by 4 and Z by 2. Beta decay: a neutron becomes a proton and an electron, 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 only reduced by thick lead or concrete; ionising power is in the reverse order.

Half-life is the time for half the nuclei in a sample to decay, so the activity also halves in each half-life.

Nuclear equations must balance nucleon numbers (top) and proton numbers (bottom) on both sides.

Fission: a heavy nucleus such as uranium-235 absorbs a neutron, splits into two lighter nuclei and releases energy plus more neutrons; used in power reactors.

Fusion: light nuclei such as hydrogen isotopes join to form a heavier nucleus, releasing energy; it needs very high temperature and powers stars.

Background radiation comes from cosmic rays, rocks, radon gas and medical or nuclear sources, and must be subtracted from counts when measuring a source's activity.