SPH3U Introduction: Units, Scientific Notation, Prefixes, Unit Conversions, Dimensional Analysis

Units There are 2 main types of units: There are 2 main systems of units: –SI System – –English System –

The SI System The international system of units consists of a set of units together with a set of prefixes. There are seven base units: Each of these base units represents, at least in principle, different kinds of physical quantities. From these seven base units, many other units are derived. In addition to the SI units, there is also a set of non-SI units accepted for use with SI which includes some commonly used units such as the litre. A coherent SI derived unit can be expressed in SI base units with no numerical factor other than the number 1. (Example to follow)

The 7 Base Units of the SI System

Derived Units Many quantities evolve from physical relationships between variables. All quantities can be represented by a base unit or combination thereof. Ex:

Prefixes A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.

Scientific Notation Scientific Notation is a convenient way of writing a really large or really small number since it eliminates any leading or trailing zeros. Standard scientific notation requires that we write only one number in front of the decimal place. When moving the decimal to the right, the exponent decreases. When moving the decimal to the left, the exponent increases. Ex)

Working with Prefixes A prefix is just another convenient way of writing a relatively large or small number. A prefix itself is NOT a unit, but can be used in conjunction with ANY unit. Typically, they are used to bring the numbers being worked with to a reasonable scale.

Working with Prefixes How many micrometers and there in a kilometer? Express in standard form without any prefixes ms

Practice Complete handout “Significant Digits, Metric Conversions” for homework.

Unit Conversions Converting units is common in solving physics problems and is necessary at times to maintain homogeneous units. Treat units like any other algebraic quantity – they can be multiplied (Eg: m x m = m^2) or divided, squared or square rooted, etc. Only quantities with identical units can be added or subtracted

Unit Conversions Example: Calculate the distance a car has traveled if it went 25 m/s for 1.5 hours. Units of time will not cancel so we must convert hours into seconds in order to end up with a unit of meters.

Converting Units Examples Convert the following: 1.1 year  s 2.5m/s^2  km/hr^2 3.7 s/m^2  hr/cm^2

Converting Units Solutions

Practice Complete the unit conversions worksheet for homework. Solutions are posted online.

Dimensions Every physical quantity requires a certain type of unit. Ex: _____________________________________ The term dimension in physics is used to refer to the physical nature of a quantity & the type of unit used to specify it. For all of mechanics (the 1 st three units of this course) there are only 3 dimensions: Length, mass, and time. By seeing how these dimensions combine in an equation we can check if the dimensions on the left balance with those on the right.

Dimensional Analysis A good way to check if an equation is valid is to check its dimensions – not units. Example: Verify that the following equation is dimensionally correct.

Practice Complete handout “Introduction to Physics Review Problems” for homework. Solutions are posted online.