IB Physics Glossary
Browse the glossary using this index
Special  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  ALL
A 

Absolute magnitude M, is a measure of how bright an object appears or the apparent magnitude, when it is observed from a distance of 10 pc. (d).  
Absorbed dose D, is the amount of energy absorbed by a unit mass of material or body tissue where D = absorbed energy/mass. Its units are Jkg^{1} or the Gray (Gy).  
Accelerationis the rate of change of velocity. (d.) $$a=\frac{\Delta v}{\Delta t} = \frac{vu}{t}$$._{}  
Accommodation is the process by which the lens in the eye can focus on both near and far objects. When we focus on distant objects the lens is longer and thinner due to the effect of the cilary muscles and the taut fibers. When we focus on nearby objects the lens becomes shorter and thicker due to contraction of the ciliary muscles.  
Accuracytells us how close the measured value of a quantity is to its true value. An accurate measurement is "close" to a true value. An inaccurate measurement is "far" from a true value.  
Acoustic impedance of a substance is the product of medium density, $$\rho$$, and speed of sound waves, c, in the medium $$Z= \rho \times c.$$ Its unit is kgm^{2}s^{1}. Impedance matching occurs when the impedance of two media are equal. The incident waves are transmitted (100%) through the media. When there is a large difference in impedance between media most of the incident sound waves are reflected.  
Adiabatic process occurs without any energy transfer to or from the gas. A rapid expansion or compression is approximately adiabatic since $$\Delta Q \approx 0$$. The 1st law of thermodynamics $$Q = \Delta U + W$$ becomes $$0 = \Delta U + W$$ or $$\Delta U =  W$$. An adiabatic expansion, $$W > 0 \Rightarrow U < 0$$, is a cooling process. An adiabatic compression, $$W < 0 \Rightarrow U > 0$$, is a heating process.  
Albedo is the ratio of total solar energy reflected back from Earth into space to the total incident solar energy. (d)  
Alpha decay $$^A_ZX \rightarrow~{}^{A4}_{Z2}Y + ^{4}_{2}\alpha$$ or $$^A_ZX \rightarrow~{}^{A4}_{Z2}Y + ^{4}_{2}He$$. Where X is the parent nucleus, Y is the daughter nucleus, A is the number of nucleons and Z is the number of protons. An example decay is $$^{241}_{95}Am \rightarrow~{}^{237}_{93}Np + ^{4}_{2}\alpha$$. Properties of alpha particles include
 
Ammeter measures current flowing through a component. It is placed in series with the component. An ideal ammeter has zero resistance so that it has no effect on the current flowing.  
Ampereis the SI unit of electrical current and is defined through the magnetic force acting between two parallel wires. If the magnetic force between two wires separated by 1m, each of length 1m, carrying equal currents, equals 2 x 10^{7} N, then the current in each wire equals 1 Ampere.

Antinodea region of maximum wave displacement. Amplitude $$2A$$.
 
Apparent brightness the energy from a star per second incident on 1m^{2} of the Earth's surface.(d)  
Apparent magnitude a measure of the brightness of a star as it appears from Earth. (d).  
Astronomical Unit is the average distance between Earth and Sun. (s)  
Attenuation is the drop in intensity as Xrays pass through a medium.  
Attenuation coefficient µ, is a constant for a material at a given Xray energy which allows us to calculate Xray intensity, I, given any thickness of material x and incident Xray intensity I_{0} where $$I = I_0 e^{\mu x}$$.  
Atwood's Machine is a pulley system with a difference in mass between the two sides of the pulley: The acceleration of the pulley, from Newton's 2nd law, is given by $$a = g \times \frac{m}{m+}$$ wherem_{} is the mass difference m_{2}m_{1}, and m_{+} is the sum of the masses m_{1}+m_{2}.  
Audiogram is a record of the variation of hearing with frequency for a patient.  
Avogadro's constant is the number of atoms in 12g of Carbon12 (6.02x10^{23}). (d)  
B 

Bacquerel , Bq, is the SI unit of activity for radioactive sources. It is equivalent to a count or disintegration per second. The activity is measured, typically, with a GeigerMuller (GM) tube.  
Beta decay $$^A_ZX \rightarrow~{}^{A}_{Z+1}Y + ^{0}_{1}\beta + ^{0}_{0}\bar{\nu}$$ or $$^A_ZX \rightarrow~{}^{A}_{Z+1}Y + ^{0}_{1}e + ^{0}_{0}\bar{\nu}$$. Where X is the parent nucleus, Y is the daughter nucleus, A is the number of nucleons and Z is the number of protons. An example decay is $$^{90}_{38}Sr \rightarrow~{}^{90}_{39}Y + ^{0}_{1}\beta + ^{0}_{0}\bar{\nu}$$. Properties of beta particles include
 
Binary to decimal conversionfor a five bitnumber $$b_4 b_3 b_2 b_1 b_0$$ the decimal equivalent is $$b_4 \times 2^4 + b_3 \times 2^3 + b_2 \times 2^2 + b_1 \times 2^1 + b_0 \times 2^0$$. An example is the binary number $$10101$$ which in decimal is $$1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 21$$.  
Binding energy is the energy required to assemble a nucleus or to separate the nucleus into its individual components/nucleons. (d) The binding energy per nucleon is the total binding energy for a particular nucleus divided by the number of nucleons contained in the nucleus. For energy to be released in a nuclear reaction, fusion or fission, the binding energy must increase. Image taken from http://www.smsec.com/en/nucl/07_1.htm  
Blind spot is a region where the optical nerve leaves the retina which does not contain rods or cones.  
Brewster's law When the angle of incidence equals Brewster's angle, the reflected and the refracted rays are perpendicular to each other. The reflected ray becomes completely horizontally planepolarized.
$$n=\tan \phi$$  
C 

Capacitanceis the ratio of charge to potential difference or voltage, $$C=\frac{Q}{V}$$. Its units are Farads.  
CCDis a charged coupled device such that the amount of charge that builds up on one of its pixels is proportional to the light intensity falling on the pixel.
The photoelectric effect is responsible for conversion of photons energy to electron energy.  
CCD resolutionis possible if the size of an image covers at least two pixels.  
CD/DVD pit depthis given by $$d = \frac{\lambda}{4}$$where $$\lambda$$ is the wavelength of the laser for the CD/DVD reader.The distance corresponds to a total additional distance of $$\frac{\lambda}{2}$$ travelled by the laser light at a pitland interface (corresponding to binary 1). DVDs (shorter pit length and double layers) have about 7 times the storage capacity of CDs. Changing or reducing the laser wavelength can increase the resolution, by decreasing $$\theta= 1.22 \frac{\lambda}{b}$$, thus allowing more pits and therefore greater storage capacity. Bluray technology uses shorter wavelength laser light.  
Chandrasekhar core limit equals 1.4 solar masses for the core of a (super) red giant. Low mass stars: core mass < 1.4 solar masses
Red giant > Planetary nebula > White dwarf Helium burns and fuses in the core into carbon and oxygen. High mass stars: core mass > 1.4 solar masses Super Red Giant > Supernova > Neutron star or Black Hole Silicon burns and fuses in the core into iron.  
Circular motionoccurs under the following conditions:
Data booklet reference: $$a\; = \;{{{v^2}} \over r}\; = \;{{4{\pi ^2}r} \over {{T^2}}}$$ $$F\; = \;{{m{v^2}} \over r}\; = \;m{\omega ^2}r$$  
Coefiicient of voume expansion $$\gamma$$, is the fractional change in volume of a substance $$\frac{\Delta V}{V}$$ per unit degree change in temperature $$\Delta T$$: $$\gamma = \frac{\Delta V}{V \times \Delta T}=\frac{V_2V_1}{V_1 \times (T_2T_1)}$$. The SI unit is K^{1}. For problems involving rise in sea level
 
Comets have a. highly elliptical orbits; b. large orbital radii beyond planets; c. orbit are in many different planes. (d)  
Conductive hearing loss occurs when the air conduction thresholds (middle ear) show a hearing loss but the bone conduction thresholds (cochlea) are normal. Reasons include
 
Conductor A material that allows the flow of electric charge through it. Conduction is the flow of charge (free electrons) from atom to atom within a material. 
Constellation is a pattern of stars, as seen from Earth, which are not close to one another in space. (d)  
Constructive interference occurs when two waves meet such that the resultant wave displacement is greater than that of the individual waves with path difference $$= n \times \lambda$$ or phase difference $$= n \times 2\pi$$. (s)  
Coulomb's Law$$F =\left( \frac{1}{4 \pi \epsilon_0}\right) \frac{q_1 q_2}{r^2} = k \frac{q_1 q_2}{r^2}$$
where F is the force exerted by particle 1 on particle 2 (and vice versa), k is the Coulomb/electric constant, 8.99 x 10^{9} Nm^{2}C^{2}, q_{1} is the charge of particle 1, q_{2} is the charge of particle 2 and r is the distance between the centres of the particles/charges.
Note $$k=\frac{1}{4 \pi \epsilon_0}$$, where $$\epsilon_0$$=8.85×10^{−12} C^{2} N^{−1}m^{−2} is the permittivity of free space. We usually just use k. We assume the charges are pointlike and all the charge is concentrated in the center. An approximation is to assume the separation of the charges, r, is much greater than their radii. The law is an inversesquarelaw, $$F \propto \frac{1}{r^2}$$. 
Critical density is the density which produces a flat universe. In a flat universe the rate of expansion of the universe gradually slows down, asymptotically approaching a zero rate of expansion. (d)  
D 

Damping involves a force that is always in the opposite direction to the direction of motion of the oscillating particle/system and the force is a dissapative force which reduces the total energy of the system. (d) Also $$\frac{E_{n+1}}{E_n}=\(\frac{A_{n+1}}{A_n}\)^2$$ the ratio of successive peak energies equals the ratio of successive amplitudes squared. For example, in the case below, the amplitude falls from 4.3 cm to 2.7 cm. Remaining energy is (2.7/4.3)^{2} = 0.394 or 39.4%.  
de Broglie wavelength is given by $$\lambda = \frac{h}{p}$$. where h is Planck's constant, and p is the momentum of a particle. Since waves behave like particles, de Broglie suggested particles can behave like waves with wavelength λ. The formula, since p = m v, and E_{K} = p^{2}/2m, can be written as $$\lambda = \frac{h}{p}=\frac{h}{mv}=\frac{h}{\sqrt{2mE_K}}=\frac{h}{\sqrt{2 m e V}}$$, where v is the velocity of the particle, E_{K} is the kinetic energy, and V is the potential difference that can accelerate a charged particle.  
Decay constant$$\lambda$$, is the probability of a radioactive decay per unit time. $$N=N_0e^{\lambda t}$$ at t=t_{1/2}, N=N_{0}/2: after one halflife the number of nuclei halves => $$\frac{N_0}{2}=N_0e^{\lambda t_{1/2}}$$ => $$\frac{1}{2}=e^{\lambda t_{1/2}}$$ or $$ 2=e^{\lambda t_{\frac{1}{2}}}$$ => $$\ln 2=\lambda t_{1/2}$$ or $$t_{1/2} = \frac{\ln 2}{\lambda}$$. A shorter halflife indicates a more active sample or a higher value for the decay constant (greater probability for a decay). A a short halflife sample can be measured from the activitytime graph, simply finding the time for the activity to fall by a factor of 2. For a long halflife sample, the activity, A, is measured at the same time as the mass, m, of the sample. We know number of atoms, N = number of moles, n, times Avogadro's constant, N_{A} and number of moles, n = mass in grams, m/atomic mass number, a, therefore $$N = \frac{m}{a} \times N_A$$ Since $$A = \lambda N$$ then $$\lambda = \frac{A}{N}$$ We can find a value for $$\lambda$$ and $$t_{1/2}$$.  
decimal to binary conversioncan be completed by dividing by 2 and keeping track of the remainder: an example is 21
which gives 10101.  
Degraded energy is transformed energy which is no longer available to perform useful work. (d)  
Derived units are not fundamental but can be expressed in terms of fundamental units.  
Destructive interference occurs when two waves meet such that the resultant wave displacement is less than that of the individual waves: path difference $$= (n+ \frac{1}{2}) \times \lambda$$ or phase difference $$= (2n + 1) \times \pi$$.  
Displacement is the linear distance of the position of an object from a given reference point. (d.) $$s=\Delta x=x_2x_1$$.  
Doppler effect is the apparent change in the frequency of a wave source due to the relative motion between the wave source and observer. Let $$f^\prime$$ = observed frequency $$f$$ = actual wave frequency $$v$$ = speed/velocity of waves in medium (fixed by medium and its properties) $$u_s$$ = speed/velocity of wave source $$u_0$$ = speed/velocity of observer For a moving source  stationary observer (change in observed wavelength of source) $$f^\prime = f \left(\frac{v}{v\pm u_s}\right)$$ Use $$\pm \rightarrow $$, $$f^\prime > f, \lambda^\prime < \lambda $$ (decrease in wavelength), if wave source moves towards observer Use $$\pm \rightarrow +$$, $$f^\prime < f, \lambda^\prime > \lambda$$ (increase in wavelength), if wave source moves away from observer For a moving observer  stationary source (change in relative speed of waves) $$f^\prime = f \left(\frac{v \pm u_0}{v}\right)$$ Use $$\pm \rightarrow +$$, $$f^\prime > f$$, increase in relative speed/velocity of waves ($$v + u_0$$), if observer moves towards wave source. Use $$\pm \rightarrow $$, $$f^\prime < f$$, decrease in relative speed/velocity of waves ($$v  u_0$$), if observer moves away from wave source. For electromagnetic waves $$\Delta f = \frac{v}{c} f$$ where v is the speed of the wave source and c is the speed of electromagnetic waves in a vacuum.  
Doppler flowspeed measurementscan be used to determine the speed of moving objects such as that of
$$U = v \frac{f^\prime  f}{f^\prime + f} = v \frac{f^}{f^+}$$ where $$f^\prime$$= measured/shifted frequency $$f$$ = actual wave frequency $$f^+ = f^\prime + f$$ $$f^ = f^\prime  f$$ $$v$$= speed/velocity of waves in medium (fixed by medium and its properties) $$U$$= speed/velocity of moving target source.  
Dose equivalent H, indicates the effective absorbed dose based on the type of ionization radiation being used. $$H = Q D$$, where is the quality factor of the ionization. The units for H is also Jkg^{1} (Gy) but we use the Sievert (Sv) to distinguish it from absorbed dose.  
E 

Eclipsing binary starsare identified by a periodic dip in their combined brightnesstime curve.  
Effective halflife the time taken for the activity of a medical radioactive isotope to reduce by half, taking into account both physical and biological removal of activity from the body such that $$\frac{1}{T_E} = \frac{1}{T_P} + \frac{1}{T_B}$$ or $$T_E = \frac{T_P \times T_B} {T_P + T_B}$$ where T_{E} is the effective halflife, T_{P} is the physical halflife and T_{B} is the biological halflife. Note the decay constants add: $$\lambda_E = \lambda_P + \lambda_B$$.  
Efficiency is the ratio of useful power of a system to the input power or the ratio of useful energy transformed to the total energy input. (d) Approximate overall energy efficiencies for different types of power station are Coal: 35%, Gas: 45% & Oil: 38%.  
Elastic collisions occur when the total kinetic energy of a system remains constant.  
Electric current is defined in terms of force per unit length between two parallel currentcarrying conductors. (d) The electric current flowing in a circuit is the rate of flow of charge, $$I = \frac{\Delta q}{\Delta t}$$.  
Electric field strengthis the force per unit charge exerted on a positive test charge placed in the field.
$$E = \frac{F}{q}=\frac{k\frac{Qq}{r^2}}{q}=k \frac{Q}{r^2}$$. Its unit is NC^{1}. It is a vector quantity and is always directed from the positive charge (+) to the negative charge () and points tangentially ($$\perp$$) to the surface of the charge.
1. An attractive force 2. A repulsive force (no field lines at centre) 3. Positive point charge to ground 4. Parallel plates (no edge effects) with constant electric field For charges of unequal magnitude, the field lines are shifted towards the lower magnitude charge. The field line pattern is pearshaped with the "apex" closer to the lower magnitude charge. The field around a charged conductor At equilibrium, the charge and electric field follow these guidelines:
For a sphere of radius R the electric field varies with distance r from centre of sphere as shown below. 
Electric Potential Difference is the work done per unit charge in moving a small positive charge between two points. (d)  
Electrical circuit symbols  
Electrical powercan be expressed in three ways $$P = V I$$ $$P = I^2 R$$  used for power dissiapation due to heating in the transmission of electricity. $$P = \frac{V^2}{R}$$.  
Electronvolt is the work done in moving an electron through a potential difference of 1 volt. (d) A charge, q, gains kinetic energy $$q V$$ when it is accelerated through a potential difference $$V$$: $$q V = \frac{1}{2}m v^2$$.  
Elevator weight is used to show how the reaction force, between a person standing in an elevator and the floor of the elevator, varies with up/down acceleration of the elevator: Note, the actual weight of the person does not change but an increase or decrease in the reaction force produces a change on the weighing scale in elevator.  
Emf or electromotive force, is the total energy supplied by a cell/battery per unit charge as it flows through the cell/battery. (d)  
Emissitivity is the ratio of power emitted (per unit area) by a body to the power emitted (per unit area) by a black body of the same dimensions at the same temperature or the ratio of power emitted by a body to the power emitted if it were a black body. (d)  
Energy density is the energy liberated per unit mass of fuel consumed. Its unit is Jkg^{1}.(d)  
Entropyis a system property that expresses the degree of disorder in the system.  
Equilibrium position is the position where a particle would remain at rest if not disturbed. (d)  
Escape velocity is the velocity that an object needs at the surface of the planet with sufficient kinetic energy to escape the gravitational attraction of the planet. $$v_{esc} = \sqrt{\frac{2GM}{R}} = \sqrt{2Rg}$$ where G is the universal gravitational constant, M is the mass of the planet, R is the radius of the planet and g is the acceleration due to gravity.For a Black Hole, the escape velocity equals c, the velocity of light in empty space. The above equation becomes $$c= \sqrt{\frac{2GM}{R}}$$ and $$R= R_s = \frac{2GM}{c^2}$$ where R_{s} is the Schwarzchild radius.  
Explosive collisionsoccur when the total kinetic energy of a system increases.  
F 

Far point is the most distant point from the eye for which the eye can focus on (assumed to be $$\infty$$).  
Faraday's law states, the induced emf is proportional to the rate of change of magnetic flux linkage: $$\epsilon \propto \frac{\Delta \Phi}{\Delta t}$$.  
First law of thermodynamics states, $$Q = \Delta U + W$$. Where Q is the heat supplied to system, $$\Delta U$$ is the change in the internal energy, W is the work done by gas, all in Joules. It is the law of conservation of energy. Note a. Q > 0, heat in; Q < 0, heat out b. $$\Delta U > 0, \Delta T > 0$$; $$\Delta U < 0, \Delta T < 0$$ c. W > 0, work done by gas; W < 0, work done on gas.  
Force fieldis a region of space where masses/charges feel a force. 
Forced oscillations occur when an object is forced to oscillate by a periodic external force. (d)  
Fuel enrichmentEnrichment is the process by which the isotopic composition of a nuclear fuel is increased to make nuclear fissions more likely. Typically, uranium fuel rods are enriched, via neutron bombardment, to ensure that the percentage content of uranium235 is increased.  
Fundamental units are the most basic units which cannot be expressed in terms of other units. The seven fundamental units are 1. meter (m); 2. second (s); 3. kilogram (kg); 4. Kelvin (K); 5. The Ampere (A); 6. mole (mol); 7. candela (cd).  
G 

g versus E
 
Galactic cluster is a collection of galaxies grouped together due to the gravitational attraction between them. (d)  
Galactic supercluster is a group of galactic clusters. (d)  
Galaxy is a large group of stars gravitationally bound together (approx. 10^{10 }stars, diameter 10^{5} ly). (d)  
Gamma decay $$^A_ZX^* \rightarrow~{}^{A}_{Z}X + ^{0}_{0}\gamma$$ where X* is an excited nucleus, X a deexcited nucleus, A is the number of nucleons and Z is the number of protons. A sample gamma decay is $$^{40}_{18}Ar^* \rightarrow~{}^{40}_{18}Ar + ^{0}_{0}\gamma$$ Properties of gamma particles include
 
Gas laws can be found, for an ideal gas, using the ideal gas equation $$P V=n R T$$. Note T is the absolute temperature and its unit is Kelvin (ºC + 273). Typical units: pressure P, Pa of kPa; volume V, m^{3} . 1. For a fixed temperature of gas (and amount of gas, ie. n fixed) $$P V = constant$$ or $$P \propto \frac{1}{V}$$. Pressure is inversely proportional to Volume.2. For a fixed volume of gas (and amount of gas, ie. n fixed) $$ P = constant \times T$$ or $$P \propto T$$. Pressure is proportional to Temperature. 3. For a fixed pressure of gas (and amount of gas, ie. n fixed) $$ V = constant \times T$$ or $$V \propto T$$. Volume is proportional to Temperature.More generally one can write $$\frac{P_2 V_2}{P_1 V_1} = \frac{n_2 T_2}{n_1 T_1}$$.  
Gravitation versus Electric Potential  
Gravitational field strength is the force per unit mass on a small (test) mass at the point. (d)
$$g = \frac{F}{m}=\frac{G\frac{Mm}{r^2}}{m}=G \frac{M}{r^2}$$.
Its unit is Nkg^{1}. It is a vector quantity and is always directed towards the centre of the mass and points tangentially ($$\perp$$) to its surface.
To compare the gravitational field strength for different masses/planets
$$\frac{g_x}{g_y}=\frac{M_x}{M_y} \left(\frac{r_y}{r_x}\right)^2$$.
 
Greenhouse effectThe atmosphere is transparent to many frequencies of electromagnetic radiation. Much of the power received from the Sun is in the visible and ultraviolet regions. This causes the surface of the Earth to warm up and radiate in the infrared (heat). Some of this infrared radiation is absorbed by gases in the atmosphere, causing the atmosphere to warm up, and reradiated in all directions. The net effect is that the atmosphere and the surface of the Earth are warmed.  
Greenhouse gases are gases in the atmosphere that absorb infrared radiation. The principle greenhouse gases are carbon dioxide ($$CO_2$$), methane ($$NH_4$$), water vapour ($$H_2O$$), and nitrous oxide ($$NO_2$$). Ozone and chlorofluorocarbons (CFCs) also contribute to the greenhouse effect.  
H 

Halflife $$t_{\frac{1}{2}}$$, is the time required for the initial activity of a radioactive sample to be reduced by a factor of 2 or the time requird for the initial number of radioactive nuclei to be reduced by a factor of 2. (d)  
Halfvalue thickness is the length of material through which Xrays must travel to reduce their intensity by 2 where $$x_{\frac{1} {2}} = \frac{ln 2} {\mu}$$, where $$\mu$$ is the attenuation coefficient.  
Heat exchangerallows the nuclear reactions to occur in a place that is sealed off from the rest of the environment. The reactions increase the temperature in the core. This thermal energy is transferred to heat water, and the steam that is produced turns the turbines.  
Hubble's law states the recessional speed, $$v$$, of a galaxy is proportional to its distance, $$r$$, from the Earth or galaxies move away from each other with a speed proportional to their separation: $$v \propto r$$ or $$v=H \times r$$, where $$H$$ is Hubble's constant.  
Hybrid vehiclesuse electric motors with a petrol engine as backup to provide additional power when necessary. Sophisticated computerized systems switch from the electric motor to the petrol engine and back as required.  
I 

Ideal gas is a gas in which the molecules do not interact or the intermolecular forces can be neglected. (d) The ideal gas equation is $$PV=nRT$$. Here we use absolute temperature, T, with unit Kelvin.  
Impulse is the change in momentum or the product of force and time: $$\Delta p = F \times \Delta t$$. (d) Its unit is N s (or kg m s^{1}).  
Inclined planeis used to show the forces acting on a block which rests, or moves, along the plane: The component of the weight down the plane is $$ m g \sin\theta$$.  
Inelastic collisionsoccur when the total kinetic energy of a system decreases.  
Insulator a material that does not allow the flow of electric charge through it. 
Internal energy of a substance is the total potential energy and random kinetic energy of the molecules of the substance. (d)  
Internal resistance of a cell/battery is the effective additional resistance that is added to a circuit by the cell/battery. This is caused by the electrical energy generated by the chemical reactions inside the cell/ battery which is dissipated within the battery when a current flows: $$\epsilon = I (R + r)$$, where $$\epsilon$$ is the emf of the cell/battery, I is the current flowing through the circuit, R is the resistance of the circuit component(s) and r is the internal resistance of the cell/battery. A graph of voltage/potential difference across external resistor (yaxis) against current flowing (xaxis) can be used to find
 
Ionization radiation is radiation composed of particles that individually carry enough energy to liberate an electron from an atom thus ionizing it. Taken from wikipedia.  
Isobaric processtakes place at constant pressure. The 1st law of thermodynamics is $$Q=\Delta U + W$$, and $$W=P \Delta V$$.  
Isochoric process occurs at constant volume. The 1st law of thermodynamics $$Q=\Delta U + W$$ becomes $$Q=\Delta U$$ (all heat converted into internal energy) since $$\Delta V = 0 \Rightarrow W = 0$$ (no work is done by gas).  
Isothermal processoccurs at constant temperature. The 1st law of thermodynamics $$Q=\Delta U + W$$ becomes $$Q=W$$ (all heat converted to work) since $$\Delta T = 0 \Rightarrow \Delta U = 0$$.  
Isotope of an element has the same number of protons (charge) but a different number of neutrons (mass). (d)  
K 

Kepler's 3rd law of planetary motion states the orbital period squared is proportional to the mean orbital radius cubed: $$T^2 \propto r^3$$. Derivation $$F = G \frac{Mm}{r^2}=\frac{mv^2}{r}$$. or $$ G \frac{M}{r}=v^2$$. Since the speed, $$v$$, is the distance travelled in one orbit, $$2 \pi r$$, divided by the orbital period $$T$$ we can write $$ G \frac{M}{r}=(\frac{2 \pi r}{T})^2$$ or $$ G \frac{M}{r}=\frac{4 \pi^2 r^2}{T^2}$$ then $$T^2 = \frac{4 \pi^2}{GM} \times r^3$$ or $$T^2 = constant \times r^3 => T^2 \propto r^3$$.  
Kinetic energyis the energy of a moving object.  
Kinetic theory of gasesis a theory which treats molecules in a gas as mechanical objects. We assume that 1. A gas contains a large number of molecules; 2. Molecules have a range of kinetic energies, and therefore a range of speeds; 3. A gas molecule occupies a volume much less than that of the volume of the gas; 4. Collisions of molecules with other molecules and with the walls of the container are elastic; 5. Molecules exert forces on other molecules or on container walls only when contact occurs; 6. Collisions times are small compared to time between collisions; 7. Molecules obey the laws of Newtonian mechanics;  
L 

Law of Conservation of Charge states that the total charge of a closed system is constant. 
Law of Conservation of Energystates, energy cannot be created or destroyed but is converted from one form into another or the total amount of energy in the universe is constant.  
Law of conservation of momentumstates, the total momentum of an system remains constant if no external forces act on the system.  
Lenz's law states the direction of the induced emf is such as to tend to oppose the change producing it. (s)
 
Lightyear ly, is the distance traveled by light in one year in a vacuum or empty space. (d)  
Linear momentum is the product of mass and velocity, $$p= m v$$. (d)  
Loglog plots are used to find the value of the exponent $$n$$ and coefficient $$a$$ for the general relationship $$ y= a x^n$$. The value of the gradient for the loglog plot equals $$n$$ and $$a= log^{1}{(\text{yintercept})}$$. For example A linear relationship should have $$n \approx 1$$; A squareroot relationship should have $$n \approx \frac{1}{2}$$; A quadratic relationship should have value $$n \approx 2$$; An inversesquare relationship should have value $$n \approx 2$$.  
LSBleast significant bit is the rightmost or the trailing bit in a binary number.  
Luminosity is the power radiated or energy radiated per unit time by a star. (d)  
M 

Magnetic fields are in the direction from North pole (N) to South Pole (S): Like poles repel: Unlike poles attract: For a straight wire carrying a current I: Use the righthandscrew rule to find the direction of Bfield For a coil carrying a current I: Looking into the coil  if direction of current is anticlockwise then the end of the coil is a North Pole (magnetic field lines exit)  if direction of current is clockwise then the end of the coil is a South Pole (magnetic field lines enter) For a solenoid carrying a current I: Looking into the solenoid  if direction of current is anticlockwise then the end of the coil is a North Pole (magnetic field lines exit)  if direction of current is clockwise then the end of the coil is a South Pole (magnetic field lines enter) 
Magnetic flux the product of magnetic flux density and area. (d)
 
Magnetic flux linkage the product of magnetic flux and number of turn. (d)
 
Magnetic forceacts on a moving charge or a current carrying conductor. We use Fleming's lefthandrule to find the direction of the magnetic force, given B and I: Note: electron displacement is in the opposite direction to conventional current I. F, B and I are perpendicular to each other. The magnetic force F acting on a charge q moving with velocity v, making an angle θ with the magnetic field of strength B is given by $$F=q v B \sin \theta$$. Only moving charged particles making an angle θ with the magnetic field "feel" the magnetic force, ie. v ≠ 0 and q ≠ 0 and θ ≠ 0. The magnetic force F acting on a current I flowing through a conductor of length L, making an angle θ with the magnetic field of strength B is given by $$F= B I L \sin \theta$$. Only current carrying conductors making an angle θ with the magnetic field "feel" the magnetic force, ie. I ≠ 0 and θ ≠ 0. 
Magnetic force on parallel wirescarrying electrical currents I can be summarized below. 
Magnetic force on wirescarrying electrical currents I can be summarized below. 
Magnification, M, is the ratio image size/object size, or $$M=\frac{L^'}{L}=\sqrt{\frac{A^'}{A}}$$ A represents area, L size/height/length.  
Magnitude of magnetic field is defined as $$B=\frac{F}{I L \sin \theta}$$ where B is the magnitude of the magnetic field, F is the magnetic force, I is the current, L is the length of conductor and θ is the angle between the currentcarrying conductor and the magnetic field.
or $$B=\frac{F}{q v \sin \theta}$$ where B is the magnitude of the magnetic field, F is the magnetic force, q is the charge, v is the velocity, θ is the angle between the path of the charged particle and the magnetic field. 
Malus' lawThe light transmitted, I, by an analyzer with incident intensity I_{0}, is given by $$I=I_0 \cos^2 \theta$$.
 
Massis the amount of matter or substance inside an object. Its value does not change with the strength of gravity. Identical objects on Earth and on the Moon have identical masses.  
Mass defect is the difference between the mass of the nucleus and the sum of the masses of its individual nucleons. (d)  
Molar mass is the mass of one mole of substance in grams. (d)  
MSBmost significant bit in a binary number is the leftmost or leading nonzero bit.  
N 

Natural frequency is the frequency at which an object will vibrate if disturbed. (d)  
Near point is the closest point to the eye on which the eye can focus.  
Newton's first law of motion an object remains stationary or remains at a constant velocity if there is no resultant force acting on the object. (s)  
Newton's Law of Gravitation$$F = G \frac{m_1 m_2}{r^2}$$
where F is the force exerted by object 1 on object 2 (and vice versa), G is the gravitational constant (6.67 x 10^{11} Nm^{2}kg^{2}), m_{1} is the mass of object 1, m_{2} is the mass of object 2 and r is the distance between the centres of the objects.
We assume the masses are pointlike and all the masses is concentrated in the center. An approximation is to assume the separation of the masses, r, is much greater than their radii. The law is an inversesquarelaw, $$F \propto \frac{1}{r^2}$$.  
Newton's second law of motion states, a resultant force acting on a body equals the rate of change of momentum of the body, $$F=\frac{\Delta p}{\Delta t}=\frac{m\Delta v}{\Delta t} = m \times a$$. (s)  
Newton's third law of motion when two bodies A and B interact, the force that A exerts on B is equal and opposite to the force that B exerts on A. (s)  
Nodea region of zero wave displacement.  
Nuclear fissionis a nuclear reaction in which large nuclei are induced to break up into small nuclei and release energy in the process.
An example of nuclear fission $$^{1}_{0}n + ^{235}_{92}U > ^{236}_{92}U > ^{144}_{56}Ba + ^{89}_{36}Kr + 3 ^{1}_{0}n$$.  
Nuclear fusionis a nuclear reaction in which small nuclei are induced to join together into larger nuclei and energy is released in the process. Nuclear fusion is the main source of the Sun’s energy.
An example of hydrogen fusion: $$^{2}_{1}H + ^{2}_{1}H > ^{3}_{2}He + ^{1}_{0}n$$.  
Nuclear modelA simple nuclear model of the atom consists of a tiny central nucleus containing all the mass and all the positive charge. The nucleus is made up of protons and neutrons. Negative electrons are kept in orbit around the nucleus as a result of the electrostatic attraction between the electrons and the nucleus. Although this simple model helps explain many atomic properties there are reasons why things cannot be this simple.  
Nucleon is a proton or a neutron. (d)  
Nuclide a type of atom that is characterized by the constitution of its nucleus / the number of protons and neutrons in the nucleus (d)  
O 

Ohm's law states that current is proportional to voltage, at constant temperature, $$I \prop V$$. (d) The graph should be a straight line passing through the origin. For nonohmic conductors current is not proportional to voltage, $$I \cancel{ \prop} V$$. The graph is nonlinear. Examples of nonOhmic conductors include
as $$I \uparrow, T \uparrow, R \uparro \Rightarrow$$ gradient is not constant, or, as $$I \downarrow, T \downarrow, R \downarrow \Rightarrow$$ gradient is not constant.
Typical graphs can be yaxis: I, xaxis: V, $$R \uparrow \Rightarrow \frac{V}{I} \uparrow \Rightarrow$$ gradient decreases;
yaxis: V, xaxis: I, $$R \uparrow \Rightarrow \frac{V}{I} \uparrow \Rightarrow$$ gradient increases.
NTC (negative temperaure coefficient): $$T \uparrow \downarrow R \downarrow \uparrow$$;
PTC (positive temperature coefficent): $$T \uparrow \downarrow R \uparrow \downarrow$$.
brightness $$\uparrow \downarrow$$, $$ R \downarrow \uparrow$$;
a variation in strain of a material (deformation per unit length due to the effect of an applied load/mass) produces a variation in electrical resistance of material
 
One Mole of substance has as many molecules as there are atoms in 12g of Carbon12. (d)  
OppenheimerVolkoff limit is approximately 23 solar masses for mass of core for Super Red Giant; for core masses < 23 solar masses (above 1.4 solar masses) $$\rightarrow$$ Neutron star for core masses > 23 solar masses $$\rightarrow$$ Black hole.  
Optically activesubstances rotate the plane of polarization of the incident light. The amount of rotation may depend on the concentration of the substance/solution and the amount/length/thickness.  
Orbital Motionoccurs when the gravitation provides the centripetal force for circular orbital motion: $$F = G \frac{Mm}{r^2}=\frac{mv^2}{r}$$.  
P 

Parallel platesFor parallel plates, of separation d, with a potential/voltage difference ΔV across the plates, the electric field, E, is given by $$E=\frac{\Delta V}{d}$$. The electric field is uniform or constant between the plates. Examples 
Parsec is the distance to a star whose parallax angle is 1 arcsecond. (d)  
Phase difference $$\phi$$, is the difference in phase angle between two oscillations with the same frequency. (d)  
Photopic vision is color vision which occurs at normal light levels. Vision is aided by the three different cone cells, S (for shortwavelengths or blue), M (for mediumwavelengths or green) and L (for longwavelengths or red).  
Polarization of light occurs when the direction of the electric field oscillations is in the same plane. (d)  
Potential divider rule is used to calculate the potential difference which is shared between components, R_{1} and R_{2}, placed in series: where $$R_1 + R_2$$ is the total resistance and E is the emf. Note $$E=V_{R1}+V_{R2}$$ for equal resistances, $$R_1=R_2$$, the potential difference is shared equally between the resistances for unequal resistances, $$R_1 \ne R_2$$, the potentail difference is not shared equally but will be greater across the resistance with highest value.  
Potential energy is a stored form of energy available to do work.  
Power is the rate at which work is done. (d)  
Precision tells us how consistent repeated measurements are. A precise set of measurements are relatively closer together. An imprecise set of measurements are spread apart.  
Pressure is the force per unit area. (d)  
Primary colors are red, green and blue. Mixed together they produce white.  
Principle of Superpostion when the paths of two waves of the same type coincide, move through each other or cross, the resultant displacement is the sum of the two individual wave displacements at the point. (s)  
Progressive travelling wave transfers energy with no net motion of the medium through which the wave travels. (d)  
Projectile motion
 
Proportional relationship $$y \propto x$$ or $$y = m x$$, occurs when the relationship between $$y$$ and $$x$$ is linear with a zero yintercept value, that is, a straight line passing through the origin. The x and yerror bars may allow a range of values for the yintercept, because the lines of max & min gradients, thus showing a possible proportional relationship for a bestfit straight line even if its yintercept value is nonzero. Beware, for the IB, a bestfit line can be any curve which fits the data points. It does not mean the bestfit straight line.  
Pulsar is a rotating neutron star. (d)  
Q 

Quality factor $$Q$$, is a measure of the ionization strength of various radioactive source.
 
Quantum efficienyis the ratio of emitted electrons to incident photons falling on a pixel.
Increasing the quantum efficiency makes the CCD more sensitive to light.  
Quasaris a quasistellar radio source. A compact region in the center of a black hole. (d)  
R 

Radioactive decay occurs when a nucleus emits an $$\alpha$$particle/ $$\beta$$particle/ $$\gamma$$particle /ionizing radiations. The process is random and spontaneous since it is unknown when a nucleus will decay. The activity is proportional to the number of undecayed nuclei. The nucleus becomes more (energetically) stable. There is a constant probability of decay. The activity/number of unstable nuclei in sample reduces by half over every halflife. It is not affected by temperature/environmental conditions.  
Radioactive decay lawis written as an exponential decay function $$N=N_0 e^{\lambda t}$$ N: #nuclei at time t N_{0}: initial number of nuclei $$\lambda$$: the decay constant  probability of a decay per unit time t: time Note $$A =  \frac{dN}{dt}= \lambda N$$ or $$A = A_0 e^{\lambda t}$$ where $$A_0 = \lambda N_0$$ A: activity at time t A_{0}: initial activity of sample $$\lambda$$: the decay constant  probability of a decay per unit time t: time  
Random error is a fluctuating error often present in experiments. It is linked to precision: imprecise data => "high" random error; precise data => "low" random error. Repeated measurements do reduce random errors. Sources of random errors can include varying reading/human error and other randomly flucuating factors which cannot be controlled during experiments.  
Rayleigh Criterion for images of two wave sources to be just resolved the maximum of one diffraction pattern is coincident with the first minimum of the other. (d)
The minimum anglular separation in the diffraction pattern, $$\theta_{min}$$ for two objects to be resolved is given by $$\theta_{min} = \frac{\lambda}{b}$$, for single slits of width b; $$\theta_{min} = 1.22 \frac{\lambda}{b}$$, for circular apertures of diameter b. If two objects at a distance r from the pupil/telescope, separated by distance s, are just resolved then, since $$s=r \theta$$, we can write $$1.22\frac{\lambda}{b} = \frac{s}{r}$$ which can be used to solve typical problems on resolution.  
Resisitvity can be found from the resisitivity equation $$R = \frac{\rho L}{A}$$, where R is the resitance, $$\rho$$ is the resistivity, L is the length and A is the crosssectional area, $$A=\pi r^2=\pi \frac{d^2}{4}$$. << Simulation >>  
Resistance is the ratio of voltage to current, $$R =\frac{V}{I}$$. (d)  
Resistance combinations occur when resistances or components are placed in series and/or in parallel combinations. The main differences between the two types of combinations are
 
Resonance occurs when an object is forced to vibrate at its natural frequency with a very large increase in amplitude. (d) Resonance is the opposite to damping. If external driving frequency, f, equals to the natural frequency, f_{0}, then f = f_{0} or f/f_{0} = 1, and resonance occurs. Notice the resonance amplitude decreases with damping, and the natural frequency decreases.  
rms voltage or current equals $$\frac{1}{\sqrt 2}$$ times the peak voltage or current. (s)
 
S 

Satellite paradox occurs when a satellite moves into a low orbit such that the frictional force increases the speed of the satellite.
 
Scalar multiplication of vectors, changes the magnitude of the vector but not the direction. For scalar $$a$$ and vector $$\vec{A}$$ with x or horizontal component $$A_H=A \cos \theta$$ y or vertical compnonet $$A_V= A \sin \theta$$ magnitude $$A=\sqrt{A_H^2 + A_V^2}$$ The multiplication $$a \times \vec{A}$$ has magnitude $$a \times A$$. The division $$\vec{A} \div a$$ has magnitude $$A \div a$$.  
Scalar quantities have magnitude only. Direction or changes in direction have no effect on scalar quantities. Examples include distance, speed, mass and temperature.  
SchönbergChandrsekhar limit states, a star leaves the main sequence when it consumes about 12% of its hydrogen fuel. (d)  
Schwarzchild radius is the distance from the centre of a black hole at which the escape velocity is equal to the speed of light in empty space, c. The radius can be found using $$R= R_s = \frac{2GM}{c^2}$$ where G is the gravitational constant, M is the mass of the black hole and c is the velocity of light in empty space.  
Scotopic vision is black and white vision which occurs in lowlight conditions. Vision is aided by the rod cells. Cone cells don't play a role.  
Second law of thermodynamicsstates that thermal energy cannot spontaneously transfer from a region of low temperature to a region of high temperature or the total entropy of the universe must always stay the same or increase.  
Secondary colors are Cyan (Blue & Green), Magenta (Blue & Red) and Yellow (Green and Red).  
Sensory hearing loss occurs when the air conduction thresholds (middle ear) and the bone conduction thresholds (cochlea) both show a hearing losses. If bone conduction losses are greater than a cochlea implant may be required. Reasons include
 
Signifiant figuresa rule, the number of significant digits in a result should not exceed that of the least precise value upon which it depends.  
Simple Harmonic Motion occurs when the acceleration (or the resultant force) on a body is directed towards equilibrium position and is proportional to its displacement from equilibrium: $$a \propto x$$ or $$F \propto x$$. (d) A typical graph for an object executing SHM is . Note 1. $$a = \omega^2 x$$; 2. $$x_0$$: amplitude/max displacement; 3. $$v_0= x_0 \times \omega$$: max velocity; 4. $$a_0= x_0 \times \omega^2$$: max acceleration; 5. $$\omega = \sqrt{\frac{k}{m}}$$, for a springmass system with stiffness k (or force per unit extension) and mass m. From Hooke's law F= k x = m a.  
Snells' law states, the ratio of the velocities of the waves in two media is equal to the ratio of the sines of the angles of incidence and refraction of the rays: $$\frac{v_1}{v_2} = \frac{sin \theta_1}{sin \theta_2}$$.  
Sound intensity is the amount of sound energy falling on a unit area per second.  
Sound intensity level (IL) , or loudness, is the response of the ear to intensity such that $$IL = 10 \hspace{3}\log_{10} \(\frac{I}{I_0}\)$$, I_{0} = 1.0 x 10^{12} Wm^{2}is the threshold for hearing.Note to add sound levels, intensities must be used not intensity levels (or loudness) with $$I = I_0 \hspace{3}\times \hspace{3} 10^{IL/10}$$.  
Specific Heat Capacity is the quantity of thermal energy required to raise the temperature of unit mass by one degree. (d)  
Specific Latent Heat is the thermal energy absorbed or released per unit mass of a substance at constant temperature during a change of phase/state. (d)  
Spectroscopic binary starsover time the spectral lines regularly split into two lines and then recombine. As one star approaches observer the other recedes leading to Doppler shifts in opposite directions. When the motion is perpendicular (to the line of sight) there is no wavelength shift;  
Speed is the rate of change of distance. (d.)  
Standing Waves vs. Travelling Waves
 
Star a massive body of gas / gas / plasma giving off light / radiant energy / electromagnetic radiation. (d)  
Stellar Cluster is a group of stars bound by gravitation in same region of space. (d)  
Surface heat capacity is the energy required to change the temperature of 1m^{2} of a planet's surface by 1 degree. (d)  
Systematic erroris a constant, "background" error often present in experiments. It is linked to accuracy: inaccurate data => "high" systematic error; accurate data => "low" systematic error. Systematic errors usually shift a the bestfit line up or down maintaining the same gradient. Repeated measurements do not reduce systematic errors. Sources of systematic errors can include miscalibrated instruments, zeroerror on instruments and/or constant human error such as readingparallax error.  
T 

Temperature absolute, is proportional to the average kinetic energy of the molecules of a substance. (d)  
The photoelectric effect is the phenomena by which electrons are emitted from the surface of a metal being illuminated with light/electromagnetic radiation. When light of different frequencies and different intensities is incident on the surface: I. There exists a frequency of light (the threshold frequency) below which no electrons are emitted whatever the intensity of the light. Energy is needed to eject the electrons from the surface. Light in this case is not behaving as a wave but as a particle (photon) since according to the wave model, the energy of a wave depends on its amplitude/intensity so one would expect emission to depend on intensity not frequency. II. For light above the threshold frequency, the emission of the electrons is instantaneous whatever the intensity of the light. Light in this case is not behaving as a wave but as a particle (photon) since according to the wave model, energy is delivered continuously to the surface so with a very low intensity wave one would expect the electrons to need a certain amount of time to gain sufficient energy to leave the surface. $$E = hf = E_K + \phi$$ where E = h f is the photon energy, E_{K }is the maximum kinetic energy of the photoelectrons and φ is the work function of the metal.We can also write $$E_K = hf  \phi$$ or with the Milikan experiment , E_{K} = eV_{s}, where V_{s} is the stopping potential $$eV_s = hf  \phi$$ or $$V_s = (\frac{h}{e})f  (\frac{\phi}{e})$$ A V_{s}f graph yields a straight with gradient = $$(\frac{h}{e})$$ and yintercept=$$(\frac{\phi}{e})$$. Or $$V_s = \frac{hc}{e} \times \frac{1}{\lambda}  \frac{\phi}{e}$$ A V_{s}1/λ graph yields a straight with gradient = $$(\frac{hc}{e})$$ and yintercept=$$(\frac{\phi}{e})$$. Notes: Consider increasing the frequency of light falling on a metallic surface while keeping the light intensity fixed. A greater stopping potential is required to reduce the photocurrent to zero. Since the energy per photon increases but the same light intensity should be maintained, the number of actual number of photons, or the photon flux is less, therefore a smaller photocurrent flows. Further reading.  
Thermal/Heat Capacity is the quantity of thermal energy required to raise the temperature of an object by one degree. (d)  
Threshold hearing curve shows that the sound intensity required to be heard is quite different for different frequencies. Most sensitive frequencies (≈ 3kHz) have lower dB values  less sound intensity is required to for the sound to be heard. Least sensitive frequencies have higher dB values  more sound intensity is required for the sound to be heard. Negative dB values indicate sound intensity is below I_{0}, the threshold intensity of hearing. The graph below shows how the curve varies with age: 20, 40 and 60 years.  
Threshold intensity of hearing is the minimum intensity at which sound is heard, I_{0} = 1 x 10^{−12} Wm^{−2}.  
Tinnitus is the sensation of ringing in the ears which can be caused by shortterm exposure to loud sounds.  
Translational equilibrium occurs when there is no resultant force on an object in any direction: $$\Sigma F = 0$$ which leads to $$a = 0 \rightarrow \Delta v = 0 \rightarrow v = \text{constant}$$.  
U 

Ultrasound Ascan is an amplitudemodulated scan with information represented as a graph of signal strength against time.  
Ultrasound Bscan is a brightnessmodulated scan with information represented as levels of brightness.  
Ultrasound choice of frequency is selected based on
$$f = 200 \lambda = 200 \frac{c} {d}$$ where c is the speed of sound waves in tissue and d is the depth of the organ/object.  
Uncertainties • resulting from measurements are combined under the following rules: addition/subtraction of quantities => add absolute errors If $$y = a \pm b \pm c $$, then $$\Delta y = \pm (\Delta a + \Delta b+ \Delta c)$$. multiplication/division of quantities = add relative/fractional/percentage errors If $$y = a \times b \times c$$, then $$\frac{\Delta y}{y} = \pm (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y(\%)= \pm (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$ and $${\Delta y} = \pm y \times (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y= \pm y \times (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$. If $$y = a \div b \div c$$, then $$\frac{\Delta y}{y} = \pm (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y(\%)= \pm (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$ and $${\Delta y} = \pm y \times (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y= \pm y \times (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$. raising quantity to n'th power = multiply relative/fractional/percentage error by n If $$y = a^n$$, then $$\frac{\Delta y}{y} = \pm n \times \frac{\Delta a}{a}$$, or, $$\Delta y(\%)= \pm n \times \Delta a(\%)$$ and $${\Delta y} = \pm y \times n \times \frac{\Delta a}{a}$$, or, $$\Delta y= \pm y \times n \times \Delta a(\%)$$.  
Unified atomic mass unit (u)is 1/12^{th} the mass of a neutral carbon12 atom.  
Uniform acceleration occurs when the acceleration $$a$$ is held constant. Since acceleration is a vector quantity, constant implies a uniform magnitude and direction for the acceleration. The equations of uniform acceleration are $$v=u + at$$ (not given on IB Physics Data Booklet) $$s = \frac{u+v}{2} t$$ $$s=ut + \frac{1}{2} a t^2$$ $$v^2=u^2 + 2 as$$ where u is the initial velocity, v is the final velocity after time t, a is the acceleration and s is the displacement.  
V 

Vector addition/subtraction $$\vec{A}$$: x or horizontal component $$A_H=A \cos \theta$$; y or vertical component $$A_V= A \sin \theta$$; magnitude $$A=\sqrt{A_H^2 + A_V^2}$$; $$\tan \theta = \frac{A_V}{A_H}$$. $$\vec{B}$$: x or horizontal component $$B_H=B \cos \theta$$; y or vertical component $$B_V= B \sin \theta$$; magnitude $$B=\sqrt{B_H^2 + B_V^2}$$; $$tan \theta =\frac{B_V}{B_H}$$. Addition $$\vec{C} = \vec{A} + \vec{B}$$: x or horizontal component $$C_H=A_H + B_H$$; y or vertical component $$C_V= A_V + B_V$$; magnitude $$C=\sqrt{C_H^2 + C_V^2}$$; $$tan \theta =\frac{C_V}{C_H}$$. Subtraction $$\vec{C} = \vec{A}  \vec{B} = \vec{A} + (\vec{B})$$: x or horizontal component $$C_H=A_H  B_H$$; y or vertical component $$C_V= A_V  B_V$$; magnitude $$C=\sqrt{C_H^2 + C_V^2}$$; $$tan \theta =\frac{C_V}{C_H}$$.  
Vector quantites have magnitude and direction. Direction or changes in direction have an effect on vector quantities. Examples include displacement, velocity, acceleration, force, momentum and field strength.  
Velocity is the rate of change of displacement. (d) $$v=\frac{\Delta s}{\Delta t}$$.  
Visual binary starsare stars of a system that are visible as separate stars (with unaided eye or through a telescope/binoculars)  
Voltmetermeasures potential difference across a component. It is placed parallel to the component. An ideal voltmeter has infinite resistance so that no current flows through it.  
W 

Wave amplitude is the maximum displacement of a particle from its rest/equilibrium position. (d)  
Wave displacement distance of an oscillating particle from its mean/equilibrium position. (d)  
Wave frequency $$f$$, is the number of oscillations of the wave source or of a particle per unit time. (d)  
Wave intensity is the rate of flow of energy across a crosssectional area perpendicular to the direction of wave propagation such that $$I \propto \text{Wave Amplitude}^2$$. (d)  
Wave period $$T$$, is the time for one complete oscillation/cycle. (d)  
Wave speed $$v$$, is the rate at which energy is transferred by the wave or the distance traveled by a wavefront per unit time. (d) $$v=\lambda \times f$$.  
Wavelength $$\lambda$$, is the distance moved by a wavefront during one oscillation of the wave source or the distance between consecutive neighboring successive points which are in phase. (d)  
Weight is the force of gravity acting on a mass: $$W=m g$$, m is the mass, g is the gravitational field strength $$\equiv$$ acceleration due to gravity. Its value does change with the strength of gravity. Identical objects on Earth and on the Moon have different weight values. Its SI unit is the Newton (N).  
Work is force × distance (moved) in the direction of the force. (d)  
Work done by a gasis given by $$W = P \Delta V$$. For an expansion, $$\Delta V > 0 \Rightarrow W > 0$$, work is done by the gas. For a compression, $$\Delta V < 0 \Rightarrow W < 0$$, work is done on the gas. Derivation Consider a gas in a closed container with a piston of area A in contact with the gas. 1. The gas expands, via some thermodynamic process, and the piston is displaced by $$\Delta x$$. 2. The gas does work on the piston (heat is converted into mechanical energy). 3. The work done is $$W=F \times s$$, ie. force x displacement: $$W = F \Delta x$$. 4. Recall the pressure exerted by the gas is given by $$P=\frac{F}{A}$$, force per unit area. Therefore $$F = P A$$.5. $$W = F \times s = (P A) \times \Delta x = P (A \Delta x) = P \Delta V$$, since $$A \Delta x$$ is the change in volume of the gas.  
Work function $$\phi$$, is the minimum energy required to liberate an electron from the surface of a metal: $$\phi = h f_0$$ where f_{0}is the minimum or threshold frequency required to produce the photoelectric effect.  