# Useful Formulae

55 54 glossary greater than greater than or equal to not equal to less than less than or equal to approx.equal to The multiplicationof aand b can be written a b,ab, or simply ab. Divisionis generally written orab rather than a b. Negative numbers a b ba a b ab ab ab ab ab ab Powers or exponents of aare defined as a3 a a a, etc. Negative and fractional exponents can also be defined,for example x2 1x2 and x12 x. The latter is the square rootof xwhich satisfies x2 x. Theaccelerationof an object is the rate of change of its velocityper unit of time, measured in unitslike metres per second per second. Angular velocity is defined to be the change in angle per unit of time. An arcis a section of a circle,measured in degrees or radians. The inverse trigonometric functions arcsin, arccos, arctan also written sin1, cos1, tan1 are such that arcsinx ,where sinx, etc. A capacitor is an electronic component which stores charge. Charge is the attribute of matter responsible for all electrical phenomena. It can take positive or negative values. The unit of charge is the coulomb. A constant is some fixed number. Physical constants involve a choice of units, whereas mathematical constants like eanddo not. Current is the flow of electric chargethrough a conductor. A degree is a unit of angular measure corresponding to 1360th of a circle. Equilibrium is a stable condition in which all forcescancel each other out. A fieldis a region of space under the influence of some measurable quantity.The field has a value and in some cases a direction at each point of the space. Force is a dynamic influence which has a tendency to produce or alter a state of motion or rest. Thefrequencyof a cyclic phenomenon is the number of cycles which occur per unit of time,the inverse of its period. ba A functionftakes valuefxfor each number x in its range of definition. Thegradient of a line is a measurement of its slope,found by dividing the vertical by the horizontal displacement. The gradient of a horizontal line is zero,and the gradient of a vertical line is not defined. The graphof the functionfplots the points x,fx on a coordinate plane. An identityis another name for an equation. An inductoris a coil which converts electric current into magnetism. A linear relation between quantities xand y is one of the form y axb. The massof an object measures its matter content,related to its weight. A parallelogramis a quadrilateral with pairs of opposite sides parallel. The periodof a cyclic phenomenon is the time taken to complete one cycle. A polygonis a closed multisided plane figure. A regular polygon has equal side lengths and equal angles between adjacent sides. Pressureis force per unit area,measured in unitslike kgcm2 or lbin2. A quadrilateral is a closed foursided plane figure. The radian is a geometrically significant unit of angular measure produced by wrappingthe radius of any circle around its circumference. This describes an angle of 3602 57.296 or 1 radian. A resistor is an electronic component which restrict the flow of current. Tensionand its opposite,compression,are measured as forces. A trapeziumis a quadrilateral with one pair of opposite sides parallel. A unit is a standardised amount of a measurable quantity. Units must be used consistently, e.g. if accelerationis taken in metressecsec,all distances covered must be measured in metres and all durations in seconds. A variableis a symbol representing a varying or unknown quantity. The velocity of an object is the distance it travels per unit time,in other words its speed,in a particular direction. Voltage is an electromotiveforce which causes a flow of current. The weight of an object is theforce produced by itsmass undergoing gravitational acceleration. We experience mass as weight. A wave is a vibration propagated through a mediumwhich involves a periodic interchange of a pair of quantities. Its periodis related to the wavelength.