SPH3U

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

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

3. 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)

4. The 7 Base Units of the SI System

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

6. 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.

7. Scientific Notation • 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)

8. 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.

9. Working with Prefixes • How many micrometers and there in a kilometer? • Express in standard form without any prefixes 0.051 ms

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

11. 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

12. 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.

13. Converting Units Examples • Convert the following: • 1 year  s • 5m/s^2  km/hr^2 • 7 s/m^2  hr/cm^2

14. Converting Units Solutions 1. 2. 3.

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

16. 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 1st 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.

17. 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.

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