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 (w)

For an object describing a circle at uniform speed, the angular velocity, w, is equal to the angle swept out by the radius in time t divided by t. UNIT: [rad] s1

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= –w^(2)x)

Simple harmonic motion (shm)
(Alternative definition)

The motion of a point whose displacement x changes with time t according to x = A sin ( t +), where A, and are constants.
[Variations of this kind are said to be sinusoidal.]

Period T for an oscillating body

The time taken for one complete cycle.

Amplitude A of an oscillating object

The maximum value of the object’s displacement (from its equilibrium position).

Phase

The phase of an oscillation is the angle (wt +e) in the equation x = A sin(wt +e) (e is called the phase constant)
UNIT: rad

Free Oscillations (Natural 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 called the system’s natural frequency.]

Damping

Damping is the dying away, due to resistive forces, of the amplitude of free oscillations.

Critical Damping

Critical damping is the case when the resistive forces on the system are just large enough to prevent oscillations occurring at all when the system is displaced and released.

Forced Oscillations

These occur when a sinusoidally varying ‘driving’ force is applied to an oscillatory system, causing it 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 large. This is resonance.

Momentum

Mass x Velocity
p=mv (Unit: kgms^(1))
It is a vector

Newton's 1st Law

An object continues moving at constant speed in a straight line, or remains at rest, unless acted upon by a resultant force.

Newton's 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.

Newton's 3rd Law

If a body A exerts a force on a body B, then B exerts an equal and opposite force on A.

The principle of conservation of momentum

The vector sum of the momenta of bodies in a system stays constant even if forces act between the bodies, provided there is no external resultant force.

Elastic collision

A collision in which there is no change in total kinetic energy

Inelastic collision

A collision in which kinetic energy is lost

Boyle's Law

For a fixed mass of gas at constant temperature, the pressure varies inversely with volume. pV=k

Ideal Gas

An ideal gas strictly obeys the equation of state pV=nRT (n=number of moles)(R=molar gas constant(8.31))(T=Temperature(Kelvin))

The Mole

The mole is the S.I. unit of ‘amount of substance’, n. It is the amount containing as many particles (e.g. molecules) as there are atoms in 12 g of carbon12.

Avogadro constant (Na)

This is the number of particles per mole. (NA=6.021023 mol1).

Internal energy, U, of a system

This is the sum of the kinetic and potential energies of the particles of the system.

Heat

This is energy flow from a region at higher temperature to a region at lower temperature, due to the temperature difference. In thermodynamics we deal with heat going into or out of a system. It makes no sense to speak of heat in a system.

Work

If the system is a gas, in a cylinder fitted with a piston, the gas does work of amount pV when it exerts a pressure p and pushes the piston out a small way, so the gas volume increases by V. Work, like heat, is energy in transit from (or to) the system.

First Law of Thermodynamics

The increase, U, in internal energy of a system is
U = Q – W in which Q is the heat entering the system and W is the work done by the system. 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 kg1 K1 or J kg1°C1

Newton’s law of gravitation.

The gravitational force between two particles is proportional to the product of their masses, m1 and m2, and inversely proportional to their separation squared, r2. F = G m1m2/r2 in which G is the gravitational constant. G = 6.67 1011N m2 kg2

Coulomb's Law

The electrostatic force, F, between two small bodies is proportional to the product of their charges, Q1 and Q2, and inversely proportional to their separation squared, r2.

Electric field strength E.

The force experienced per unit charge by a small positive charge placed in the field. Unit: V m1 or N C1.

Gravitational field strength g.

The force experienced per unit mass by a mass placed in the field. Unit: m s2 or N kg1.

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. [= JC1]

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: Jkg1.

Kepler’s laws of planetary motion: 1

Each planet moves in an ellipse with the Sun at one focus.

Kepler’s laws of planetary motion: 2

The line joining a planet to the centre of the Sun sweeps out equal areas in equal times.

Kepler’s laws of planetary motion: 3

T2, the square of the period of the planet’s motion, is proportional to r3, in which r is the semimajor axis of its ellipse. [For orbits which are nearly circular, r may be taken as the mean distance of the planet from the Sun.]

Dark matter

Matter which we can’t see, or detect by any sort of radiation, but whose existence we infer from its gravitational effects.

Radial velocity of a star [in the context of Doppler shift]

This is the component of a star’s velocity along the line joining it and an observer on the Earth.
