Dimensions & Unit Conversions

1. Dimensions & Unit Conversions August 11 / 12, 2014

2. Dimensions & Units • All physical quantities have dimensions and are expressed in units. • Dimension describes what the physical quantity is • Units are how the quantity is measured Example: Speed Speed has the dimensions of Length / Time Speed may be measured by a variety of different units (e.g. mph, km/s, etc.) You can convert between different units of the same physical quantity (e.g. seconds into hours) but CANNOT convert one dimension into another (e.g you can’t convert time into length)

3. In the study of mechanics, we will work with physical quantities that can be described in terms of three dimensions: • length (L), time (T) , and mass (M). • Thecorresponding basic SI- units are: • Length– 1 meter (1m) is the distance traveled by the light in a vacuum during a time of 1/299,792,458 second. • Mass – 1 kilogram (1 kg) is defined as a mass of a specific platinum-iridiumalloy cylinder kept at the International Bureau ofWeights and Measures at Sevres, France • Time – 1 second (1s) is defined as 9,192,631,770 times the period of oscillation of radiation from the cesium atom.

4. ALLphysical dimensions can be expressed in terms of combinations of seven basic dimensions, which can be measured directly. Deriveddimensions are combinations of 7 basic ones. Basic Physical Quantity Derived Physical Quantity Derived Dimension Derived SI Unit Basic Dimension Basic SI Unit

5. Go back to the measurements you did earlier & fill in the rest of the table

6. base unit 1 • femtopiconano micro mili kilo mega gigatera • fp n m m k M G T 10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 centideci c d 10-2 10-1 Larger units Smaller units every step is 10±1 power They are grouped into steps 10±3

7. 1 • fp n m m k M G T 10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 c d 10-2 10-1 SI conversions! larger unit → smaller number The problem: We have to convert 5 into kl. Will the number in front of kl be smaller or bigger? Smaller!!

8. 1 • fp n m m k M G T Moving the decimal seems so much easier … why do we both with conversion factors? Because sometimes moving the decimal won’t work … more on this later! 10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 c d 10-2 10-1 SI conversions! larger unit → smaller number We can do SI unit conversions in two different methods: = 1 Method 1: Conversion factors * Note: The larger unit always has a 1 in the conversion factor (i.e. 1 kℓ and 1 km). Method 2: Moving the decimal

9. 1 • fp n m m k M G T 10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 c d 10-2 10-1 Another problem! smaller unit → bigger number Will the number in front of cm be smaller or bigger? larger!! = 1 Method 1: Conversion factors Method 2: Moving the decimals

10. One more as a class … The wavelength of green light is 500 nm. How many meters is this? or

11. Practice using both methods on your whiteboard … hold it up when you are done I have 906 gigabyte hard drive on my computer. How many bytes of data will it hold? 9.06 X 1010 bytes Now practice more. If you are confident, do them by yourself. If you are not confident, then work with someone who is confident. BUT, the less confident one should be the one leading the practice and talking out their process!!!!

12. Practice 1: Basic SI conversions • How many liters is 16 ℓ ? • 4.3 x 104 ns = ? µs • 5.2 x 108ms = ? Ks • 0.09 cm = ? pm 4.3 = 43 µs 5pm

13. = 7.2 x When do you need to use conversion factors? • When converting between SI and English units • When converting between units that have exponents Example 1: 20 m/s → km/h Example 2: 7.2 m3 → mm3 20 = 20 = 72 km/h

14. Let’s do two as a class … = 10-7m3 Problem 1: Problem 2: 100 mm3 → m3 60 mi/h = ? m/s HINT: 1 mi = 1609 m 60 = 27 m/s

15. Practice onyour whiteboard … hold it up when you are done 75= 750 kg/m2 75 g/cm2 → kg/m2 Now practice more (use homework).. If you are confident, do them by yourself. If you are not confident, then work with someone who is confident. BUT, the less confident one should be the one leading the practice and talking out their process!!!!

16. Closure • What were our objectives today and how did we meet them? • How did what we do today reflect our statement of inquiry? • What was our learner profile trait, and how did we demonstrate it?

17. Exit Ticket • 0.05 cm = _______ mm • 9.3 X 105 nm = __________ mm • 3.5 m / s = __________ km / hr • 35 m2 = __________ km2 Bonus: What is the difference between systematic and random error?