Cambridge A-Level Definitions

This post contains the definitions used in the A-level curriculum.

A-level Definitions

Motion in a circle

Radian

One radian is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius.

Angular speed

The angular speed is defined as the angle swept out by the radius per second.

Angular velocity

The angular velocity is defined as the angle swept out in a certain direction (e.g. clockwise or anticlockwise) by the radius per second.

Simple Harmonic Motion

Simple harmonic motion

Simple harmonic motion is defined as the motion of a particle about a fixed point such that its acceleration is proportional to its displacement from the fixed point and is directed towards the point.

Period

Period is the time taken for the oscillator to complete one oscillation.

Frequency

Frequency is the number of oscillations completed per unit time

Displacement

Displacement is the distance of the oscillator from equilibrium position

Amplitude

Amplitude is the maximum displacement of the oscillator from equilibrium position

Free oscillation

An object is said to undergo free oscillation if the only external force acting on it is the restoring force

Damped oscillation

An object is said to undergo damped oscillation if friction and other forces, other than the restoring force, also acts on the object such that the oscillator energy is eventually converted to heat.

Resonance

Resonance occurs when the natural frequency of vibration of an object is equal to the driving frequency, giving a maximum amplitude of vibration

Phase

Phase refers to the point that an oscillating mass has reached within the cycle of a complete oscillation

Phase difference

Phase difference is the fraction that one wave is out of step with another wave. It can be measured in fraction, radians or degrees

Gravitational Field

Newton’s law of gravitation

Newton’s law of gravitation states that two point masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of their separation

Gravitational field

Gravitational field is a region which a mass experiences a gravitational force

Gravitational field strength

The gravitational field strength at a point is defined as the force per unit mass acting on a small mass placed at that point

Gravitational potential

Gravitational potential at a point is defined as the work done by an external agent in bringing unit mass from infinity to the point

Kepler’s third law of planetary motion

For planets describing circular orbits about the same central body, the square of the period is proportional to the cube of the radius of the orbit

Geostationary orbit

A geostationary orbit is an equatorial orbit with the same period of revolution as the Earth rotation and move in the same direction as the Earth rotation

Electric field

Law of electrostatic charges

Like charges repel, unlike charges attract

Coulomb’s law

The force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them

Electric field

Electric field is a region which a charge experiences an electric force

Electric field strength

Electric field strength at a point is the force per unit charge acting on a small positive charge placed at that point

Electric potential

Electric potential at a point is defined as the work done by an external agent in bringing unit positive charge from infinity to that point

Relationship between field strength and potential

The field strength is equal to the negative of the potential gradient at that point

Capacitance

Capacitance is the ratio of charge to potential for a conductor

Farad

One farad is one coulomb per volt

Factors affecting capacitance of a pair of parallel plates

The capacitance is directly proportional to the area of the plates and inversely proportional to the distance between them

Relative permittivity

The relative permittivity is defined as the capacitance of a parallel-plate capacitor with a dielectric between the plates divided by the capacitance of the same capacitor with a vacuum between them,

Time constant of a capacity

The time constant of a capacitor is the time for the charge to decrease to 1/e of its initial charge

Temperature

Kelvin

One kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water

Equation of state of a gas

The volume of a gas is inversely proportional to its pressure, provided that the temperature is held constant

Charles’ law

For a given mass of gas maintained at constant pressure, the volume of the gas is directly proportional to its thermodynamic temperature

Pressure law/Gay-Lussac’s law

For a given mass of gas maintained at constant volume, the pressure of the gas is directly proportional to its thermodynamic temperature

Mole

The mole is the amount of the substance which contains as many elementary particles as there are atoms in 12 g of carbon-12

Avogadro constant

Avogadro constant is the number of atoms in 12 g of carbon-12. It has a value of 6.02 × 1023 per mole.

Ideal gas

An ideal gas is a gas which obeys the equation of state pV = nRT at all temperatures, pressures and volumes

Root-Mean-Square speed

R.M.S. speed of a molecule is the average speed of an ensemble of molecules obtained by the square root of the mean of the squared-speeds of all the molecules

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Mean of the square speeds of all the molecules in the gas system

Assumptions of an ideal gas

  1. All molecules behave as identical, hard, perfectly elastic spheres.

  2. The volume of the molecules is negligible compared with the volume of the container.

  3. There are no forces if attraction or repulsion between molecules.

  4. There are many molecules, all moving randomly.

First law of thermodynamics

The increase in internal energy of a system is equal to the sum of heat added to the system and the work done on it

Alternating Current

Root-Mean-Square value

The r.m.s. value of the current or voltage is that value of the direct current or voltage that would produce heat at the same rate in a resistor

Rectification

Rectification is the process of converting an alternating current to a direct current

Smoothing

Smoothing is the process of reducing the fluctuations in the unidirectional output of an a.c. voltage

Magnetic field

Law of magnets

Like poles repel. Unlike poles attract

Motor effect

Motor effect is the phenomenon when a current-carrying conductor is at an angle to a magnetic field and experiences an electromagnetic force

Magnetic field

Magnetic field is a region which a magnetic pole experiences a magnetic force

Magnetic flux

Magnetic flux is the product of the magnetic flux density and the area normal to the lines of flux

Weber

One weber is the magnetic flux such that when linking to a circuit of one turn, an e.m.f. of 1 V will be induced in the circuit when the magnetic flux is reduced at a uniform rate to zero in one second

Magnetic flux density

Magnetic flux density is numerically equal to the force per unit length acting on a conductor carrying unit current at right angle to a magnetic field

Tesla

One tesla is the magnetic flux density which, acting normally to a long straight wire carrying 1 A current, causes a force per unit length of 1 N m–1 on the conductor

Magnetic flux linkage

Magnetic flux linkage is the product of the number of turns of a conductor and the magnetic flux passing through the conductor

Faraday’s law of electromagnetic induction

The e.m.f. induced is proportional to the rate of change of magnetic flux linkage

Lenz’s law

The direction of the induced e.m.f. is such as to cause effects to oppose the change producing it

Photoelectric effect

Photoelectric effect

Photoelectric effect is the emission of electrons from the surface of a metal when electromagnetic radiation is incident on its surface

Observations from photoelectric effect

  • If photoemission takes place, it does so instantaneously. There is no delay between illumination and emission.

  • Photoelectric emission takes place only if the frequency of the incident radiation is above a certain minimum value called the threshold frequency.

  • Different metals have different threshold frequencies.

  • Whether or not emission takes place depends only on whether the frequency of the radiation is above the threshold for that surface. It does not depends on the intensity of radiation.

  • For a given frequency, the rate of emission of photoelectrons is proportional to the intensity of the radiation.

Conclusion from photoelectric effect

  • The photoelectrons have a range of kinetic energies, from zero up to some maximum value. If the frequency of the incident radiation is increased the maximum kinetic energy of the photoelectrons also increases.

  • For constant frequency of the incident radiation, the maximum kinetic energy is unaffected by the intensity of the radiation.

  • When the maximum kinetic energy of the photoelectrons is zero, the minimum frequency required to cause emission from the surface may be found.

Photon

A photon refers to a quantum of energy when the energy is in the form of electromagnetic radiation

Work function

Work function energy is the minimum amount of energy necessary for an electron to escape from the surface of a metal

Nuclear Physics

Half-life

The half-life of a radioactive nuclide is the time taken for the number of undecayed nuclei to be reduced to half its original number

Activity

The activity of a radioactive source is the number of nuclear decays produced per unit time in the source. Activity is measured in becquerels (Bq), where 1 Bq is 1 decay per second

Decay constant

Decay constant is defined as the probability per unit time that a nucleus will undergo decay

Atomic mass unit

One atomic mass unit is defined as being equal to 1/12 of the mass of a carbon-12 atom

Mass defect

Mass defect of a nucleus is the difference between the total mass of the separate nucleons and the combined mass of the nucleus

Binding energy

Binding energy is the energy equivalent of the mass defect of a nucleus. It is the energy required to separate to infinity all the nucleons of a nucleus

Binding energy per nucleon

Binding energy per nucleon is defined as the total energy needed to completely separately all the nucleons in a nucleus divided by the number of nucleons in the nucleus

Nuclear fission

Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei of approximately the same mass

Observation from probing matter with alpha particles(Rutherford scattering)

  • the vast majority of the alpha-particles passed through the foil with very little or no deviation from their original path

  • a small number of particles were deviated through an angle of more than about 10º.

  • an extremely small number of particles (one in ten thousand) were deflected through an angle greater than 90º.

Conclusions from probing matter with alpha particles

  • the majority of the mass of an atom is concentrated in a very small volume at the centre of the atom. Most alpha-particles would therefore pass through the foil undeviated.

  • the centre of an atom is positively charged. Alpha-particles which are also positively charged, passing close to the nucleus will experience a repulsive force causing them to deviate.

  • Only alpha-particles that pass very close to the nucleus, almost striking it head-on, will experience large enough repulsive forces to cause them to deviate through angles greater than 90º. The fact that so few particles did so confirms that the nucleus is very small, and that most of the atom is empty space.

  • Because atoms are neutral, the atoms must contain negative particles. These travel around the nucleus

Direct Sensing

Properties of an ideal op-amp

  • infinite input impedance

  • zero output impedance

  • infinite open-loop gain

  • infinite bandwidth

  • infinite slew rate

Virtual earth

In a inverting negative feedback circuit, the negative input voltage would tend towards the value of the non-inverting input, which is earthed. Hence, the inverting input is very close to 0 V. This input is said to be virtual earth.

Remote Sensing

Intensity

Intensity is the wave power per unit area normal to wave direction

Hardness(X-ray)

Hardness is the penetration of the X-ray beam, which determines the fraction of the intensity of the incident beam that can penetrate the part of the body being X-rayed

Sharpness(X-ray)

Sharpness is related to the ease with which the edges of structure can be determined

Contrast(X-ray)

Contrast refers to the range of blackening in an X-ray image. Good contrast has a wide range of blackening

Half-value thickness

Half-value thickness is the thickness of medium that will reduce the intensity of X-ray beam by half

Tomography

Tomography is a technique whereby a three-dimensional image through a body may be obtained

Specific acoustic impedance

Specific acoustic impedance is the product of the density of the medium and the speed of the wave in the medium

Communication

Modulation

Modulation is the variation of either the amplitude or frequency of the carrier wave

Amplitude modulation

In amplitude modulation, the carrier wave has constant frequency. The amplitude of the carrier wave is made to vary. These variations are in synchrony with the displacement of the information signal

Frequency

In frequency modulation, the amplitude of the carrier wave remains constant. The frequency of the carrier wave is made to vary in synchrony with the displacement of the information signal

Attenuation

Attenuation is the decrease in signal strength as it travels over a distance

Bandwidth

The bandwidth is the range of frequencies that the signal occupies

Analogue signal

An analogue signal can have any value, within limits, and is an exact representation of the raw information

Digital signal

A digital signal consists of a series of ones and zeros, with no values between them

Bit

Each digit in the binary number is known as a bit

Noise

Noise is the random, unwanted signal that adds to and distorts a transmitted signal

Sampling

Sampling is the measurement of the analogue signal at regular time intervals

Analogue-to-digital converter

In an ADC, the analogue voltage is sampled at regular intervals of time, at what is known as the sampling frequency or sampling rate. The value of the sample voltage measured at each sampling time is converted into a digital number that represents the voltage value

Digital-to-analogue converter

In a DAC, a digital signal is converted into an analogue signal

Characteristics of wire-pair cable

  • used mainly for short-distance communication

  • cause high attenuation of signal

  • easily pick up noise

  • suffer from cross-talk and are of low security

  • have limited bandwidth

 

Comparing a wire pair and coaxial cable

The coaxial cable

  • is more costly

  • causes less attenuation

  • is less noisy and is more secure

  • has a larger bandwidth

Advantages of fibre optics

  • large bandwidth, giving rise to large transmission capacity

  • much lower cost than metal wire

  • diameter and weight of cable is much less than metal cable, hence easier handling and storage

  • much less signal attenuation, so far fewer regenerator amplifiers are required, reducing the cost of installation

  • do not pick up electromagnetic interference, so very high security and negligible cross-talk

  • can be laid alongside existing routes such as electric railways lines and power

Geostationary satellites

Geostationary satellites are satellites orbiting the Earth with a period of 24 hours at a height of 3.6 × 104 km above the Earth’s surface. The satellites orbit in the same direction as the rotation of the Earth (from west to east) and the orbit is above the equator

Polar satellites

Polar satellites are satellites that have low orbits and pass over the poles