UNITS AND DIMENSIONS

SI units

Why Do we need Units?

•      We need units because we want to measure the amount or quantity of some things.

•      To make this measurement globally acceptable we need to put some unique measurement value. This value is called a UNIT.

The International System of Units (SI)

	UNIT NAME	UNIT SYMBOL	DERIVED FROM	QUANTITY	NAMED AFTER
All lower case unit symbols	Meter	m		Length
	kilogram	kg		Mass
	Second	s		Time
	Candela	cd		Luminous intensity
	Mole	mol		Amount of substance
	liter	l, L	10-3 m3	volume
Leading capital letter in unit symbol	ohm		WA-2	resistance
	Ampere	A		Electric current
	Kelvin	K		Thermodynamic temperature
	Hertz	Hz	s-1	Frequency
	Newton	N	Kgms-2	Force
	Joule	J	Nm	Energy
	Watt	W	Js-1	power
	Volt	V	WA-1	voltage

1.1.2 SI Prefixes

DIMENSIONS
There are three main dimensions we are using.
1. Dimension of length - [L]
2. Dimension of mass - [M]
3. Dimension of time - [T]

By using the above basic dimensions it can be expressed any derived quantity.

Dimensional Analysis

Dimensional Analysis can be used to,
     1. Checking for Dimensional Consistency
Example:

     2. Generate Equations
Example:

We want to know how the speed of waves, v, on a string depends its mass m, length l, and tension Q? We can solve this problem using dimensional analysis.

First work out the dimensions of all the terms: