Period T for a point describing a circle: Time taken for one complete circuit.
Frequency f: The number of circuits or cycles per second.
Angular velocity ω: For a point describing a circle at uniform speed, the angular velocity ω is equal to the angle θ swept out by the radius in time t divided by t . (ω= θ/t) UNIT: [rad]
Simple harmonic motion (shm): Shm occurs when an object moves such that its acceleration is always directed toward a fixed point and proportional to its distance from the fixed point. (a=-ω2x)
Simple harmonic motion (shm): (Alternative definition): If the displacement x of a point changes with time t according to the equation x = a sin(ωt+ε) where a, ω and ε are constants, the motion of that point is shm. [Variations of this kind are said to be sinusoidal because they are determined by a sine term.]
Period T for an oscillating body: Time taken for one complete cycle.
Amplitude A of an oscillating object: The maximum value of the objects displacement (from its equilibrium position).
Free oscillations: Free oscillations occur when an oscillatory system (such as a mass on a spring, or a pendulum) is displaced and released. [The frequency of the free oscillations is known as the natural frequency.]
Damping: Damping is the dying away of amplitude with time of free oscillations due to resistive forces.
Forced oscillations: These occur when a sinusoidally varying force is applied to an oscillatory system, causing the system to oscillate with the frequency of the applied force.
Resonance: If, in forced vibrations, the frequency of the applied force is equal to the natural frequency of the system (e.g. mass on spring), the amplitude of the resulting oscillations is very large. This is resonance.
Momentum: The momentum of an object is its mass multiplied by its velocity. (p = mv). It is a vector. UNIT: kg m s
Newtons Laws of Motion: 1st Law: An object continues in a state of uniform motion in a straight line, or remains at rest, unless acted upon by a resultant force.
Newtons Laws of Motion: 2nd Law: The rate of change of momentum of an object is proportional to the resultant force acting on it, and takes place in the direction of that force.
Newtons Laws of Motion: 3rd Law: If an object A exerts a force on a second object B, then B must exert a force which is equal in magnitude but opposite in direction on A.
Elastic collision: A collision in which there is no loss of kinetic energy.
Inelastic collision: A collision in which kinetic energy is lost.
Work: Work done by a force is the product of the magnitude of the force and the distance moved in the direction of the force.( W.D. = Fxcosθ) UNIT: joule (J) [= Nm]
Hookes Law: The extension of an elastic object such as a wire or spring is proportional to the stretching force, provided the extension is not too large. (F = kx).
Energy: The energy of a body or system is the amount of work it can do. UNIT: joule (J).
Power: This is the work done per second, or energy converted or transferred per second. UNIT: watt (W) [= Js-1].
Conservation of energy: Energy cannot be created or destroyed, only transformed from one form to another.
Potential energy: This is energy possessed by virtue of position. (e.g. Gravitational PE = mgh)
Efficiency: % Efficiency = 100×(Useful energy obtained)/(Total energy input).
Internal energy: The internal energy (of say a container of gas) is the sum of the potential and kinetic energies of the molecules.
Thermodynamics. First Law: The heat supplied to a system (e.g. a mass of gas) is equal to the increase in internal energy plus the work done by the system. (Q = ∆U + W). [The law is essentially a restatement of the law of conservation of energy including heat as an energy form. Any of the terms in the equation can be positive or negative, e.g. if 100 J of heat is lost from a system Q = 100 J]
Specific heat capacity c: The heat required, per kilogram, per degree Celsius or Kelvin, to raise the temperature of a substance. UNIT: J kg-1 K-1 or J kg-1°C-1
Mole: This is the amount of substance that has the same number of particles (usually atoms or molecules) as there are atoms in exactly twelve grammes of the nuclide C 12 .
Avogdadro constant NA: This is the number of particles in a mole. (NA=6.02×1023 to 3 figs). \
Boyles law: For a fixed mass of gas at constant temperature, the pressure varies inversely as the volume. (p = k/V)
Ideal gas: An ideal gas strictly obeys the equation of state pV = nRT.
Capacitor: A pair of parallel metal plates, a small distance apart, insulated from one another.
Relative permittivity εr.of an insulator or dielectric: If capacitance is measured first with vacuum between the plates and then with a slab of insulator between, the capacitance increases by a factor εr
Root mean square value (r.m.s.): This is a form of average, which is really self defined. Thus for three discrete quantities 1,2 and 3, the r.m.s value is given by (()) 2163312 222 /. +=+ . For sinusoidal variations the r.m.s. value over a complete cycle is given by the peak (maximum) value divided by 2. (e.g. Irms =IO/ 2) 3.4.6(e)
Capacitor, reactance of: When an AC voltage is applied to a capacitor, the reactance is given by XC = Vrms/Irms where Vrms and Irms are, respectively, the voltage across and the current ‘through’ the capacitor. It is equal to 1/ ω C (or 1/2πfC).
Inductor, reactance of: When an AC voltage is applied to an inductor, the reactance is given by XL = Vrms/Irms where Vrms and Irms are, respectively, the voltage across and the current through the inductor. It is equal to ω L (or 2πfL)
Newtons law of gravitation: The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the distance between their centres. F = Gm1m2/r2
Electric field strength E: The force experienced per unit charge by a small positive charge placed in the field. Unit: Vm-1.
Gravitational field strength g: The force experienced per unit mass by a mass placed in the field. Unit: ms-2 or Nkg-1.
Electric potential VE: Electric potential at a point is the work done per unit charge in bringing a positive charge from infinity to that point. Unit: V. [= JC-1]
Gravitational potential Vg: Gravitational potential at a point is the work done per unit mass in bringing a mass from infinity to that point. Unit: Jkg-1.
Magnetic flux density B: A length l of wire perpendicular to a magnetic flux density B, carrying a current I, experiences a force of magnitude BIl. Unit: T (Tesla) [= NA-1m-1]
Relative permeability r: When magnetic material of relative permeability r fills a long solenoid, the magnetic flux density in the material is given by B = rB0 where B0 is the flux density when the solenoid is evacuated.
Ampere A: The ampere is that constant current which when flowing through two infinite, thin, parallel wires, one metre apart in vacuum, produces a force between the wires of 2×10-7N per metre of length. Unit: A.
Magnetic flux φ Weber Wb: If a single-turn coil of wire encloses an area A, and a magnetic field B makes an angle θ with the normal to the plane of the coil, the magnetic flux through the coil is given by Ф = AB cos θ. Unit: Wb=Tm2.
Flux linkage NФ: If the above coil consists of N turns, the flux linkage is given by NФ . Unit: Wb or Wb turn.
Faradays law: When the flux linking an electrical circuit is changing, an emf is induced in the circuit of magnitude equal to the rate of change of flux.
Lenzs Law: The direction of any current resulting from an induced emf is such as to oppose the change in flux linkage that is causing the current.
Self inductance L: Henry H When a current I through a coil produces a flux linkage NФ, the self inductance of the coil is given by L= NФ/I. Unit: H=WbA-1=Tm2A-1 [= VsA-1]
α radiation: A stream of helium He 4 2 nuclei.
β radiation: A stream of electrons.
γ radiation: Short wavelength electromagnetic radiation (shorter than X-rays).
Half life:The time taken for the number of radioactive nuclei N (or the activity A) to reduce to one half of the initial value. Unit: s.
Activity A. Becquerel Bq: The rate of decay (number of disintegrations per second) of a sample of radioactive nuclei. Unit: Bq=s-1
Decay constant λ: The constant which appears in the exponential decay law t NeN −λ = 0 and determines the rate of decay (the greater λ is, the more rapid the rate of decay). It is related to half life by λ = ln2/ 1 2 T . Unit: s-1
Radioisotopes: Isotopes (of the same element) have the same atomic number Z but different mass number A. Radioisotopes are simply isotopes which are radioactive.
Unified atomic mass unit u: The unified atomic mass unit is defined as exactly one twelfth of the mass of one atom of carbon 12. Thus one atom of C 12 has a mass of exactly 12u. (1u = 10-3 / NA = 1.66x10-27kg)
Electron volt (eV): This is the energy transferred when an electron moves between two points with a potential difference of 1 volt between them. 1 eV = 1.6 × 10-19 J [Within the context of particle accelerators it can also be defined as: the energy acquired by an electron when accelerated through a pd of 1V.]
Binding energy of a nucleus: The energy that has to be supplied in order to dissociate a nucleus into its constituent nucleons. [It is therefore not energy which a nucleus possesses.] Unit: J [or MeV]
De Broglie relationship λ = h/p: The key relationship relating to wave-particle duality. It gives the wavelength λ associated with a moving particle in terms of its linear momentum p and the Planck constant h.
