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1. Units and Measurement

1.1 Introduction

Measurement of physical quantities such as time and distance form the basis of physics. In our everyday experience, we make use of physical quantities for various purposes -- we use clocks and time for scheduling, we use distances and speeds while driving, and we talk about the square-foot (area) of our apartments or homes. Square-foot (or \(ft^2\)), while a commonly used unit, is not a SI unit. The SI units (or metric units) are a widely accepted standard of units used around the world and in most scientific fields including physics.

The unit for a physical quantity such as speed (SI unit: \(m/s\)) can be written down in terms of the units for length (SI unit: \(m\)) and for time (SI unit: \(s\)). Such physical quantities that can be defined in terms of base physical quantities are called derived quantities. The following base quantities and their corresponding SI units are defined in the SI (metric) system:

Base quantities and their SI units

meter (\(m\))

kilogram (\(kg\))

second (\(s\))

ampere (\(A\))

kelvin (\(K\))

mole (\(mol\))

candela (\(cd\))

In this course, we will mostly make use of four base quantities: length, mass, distance and time. In addition to these base quantities, we will also look at various derived physical quantities derived from these, such as speed, acceleration and force.

1.2 Common prefixes in the metric system

Prefixes to describe small quantities

\(10^{-2}\)

\(10^{-3}\)

\(10^{-6}\)

\(10^{-9}\)

\(10^{-12}\)

\(10^{-15}\)

Prefixes for large quantities

\(10^3\)

\(10^6\)

\(10^9\)

\(10^{12}\)

1.3 Unit conversion

Examples of unit conversion

\[ 65\ {\rm miles/hr} = 65 \times \frac{\rm mile}{\rm hr} = 65 \times \frac{\rm mile}{\rm hr} \times \frac{1.61\ \rm km}{1\ \rm {mile}} = 104.65\ {\rm km/hr}\]
\[ 90\ {\rm km/hr} = 90 \times \frac{\rm km}{\rm hr} \times \frac{1000\ m}{1\ \rm km}\times \frac{1\ \rm hr}{3600\ s} = 25\ m/s\]