1. Physics Tools and Standards
Each discipline has a language.
The language of physics is math!
What are the mathematical tools you need to succeed?

2. Measurements We need a way to standardize measurements
Compare to a known quantity
Must be constant, repeatable, and agreed upon by all users

3. Measurements Constant, repeatable, agreed upon Divide into groups of 3
What is the size of the lab tables?
What is the time it takes for a pencil to fall from the 2nd story to the ground?

4. Measurements Was your data reproducible? How could you test this?
How did you agree upon the standard?
Did you use estimates if your measurement was not an exact number of your standard? How did you estimate?
How accurate were you? How could you be more accurate?

5. Metric System and SI Units
Standard measurements based on powers of 10
SI units standardized and accepted by scientists worldwide
All your answers will include the SI unit!

6. Derived units are combinations of the base units.
Ex: speed is measured in meters per second or m/s

7. SI Prefixes

9. How To: Converting Units
Remember factor-label method?
Multiply your quantity in one unit by a conversion factor that =1 to convert to another unit
REMEMBER- units are your friend! Keep them involved and you will succeed.

10. How to: Converting Units
Ex: convert 10 m to cm
1. Draw a big T
2. Put your starting number in the top left and its same unit in the bottom right

11. How to: Converting Units
3. Write the unit that you want in the top right
4. Add numbers to your conversion factor to make it =1. (how many cm in a m or vice versa)

12. How to: Converting Units
5. Multiply through and cross out units that cancel out.
*** You can do these conversions in multiple steps***

13. Practice Problems
p. 7 #5-8

14. UNITS ARE YOUR FRIEND!!!
Treat units as algebraic quantities in your calculations and keep them superglued to their numbers!
When you do this and the units of your answer are correct, then your answer should be as well.

16. Scientific Notation
Really big or really small numbers can be a bummer to write and work with
You can get either really big numbers by using positive powers like 1 x 105 =
You can also show really small numbers by using negative powers like 1 x 10-5 =
Don’t worry about using your calculator to figure out what these mean- just move the decimal point left (negative exponent) or right (positive exponent) the number of spaces given by the exponent

17. The Power of Powers
Powers of 10 used in scientific notation mean big differences in the value of a number
For example:
106 sec is about 12 days
109 sec is about 32 years
1012 sec is about years!

18. How to Read Scientific Notation
Now try 2 x 10-9

19. How to Write Scientific Notation
Move decimal so only 1 nonzero # is to the left of the decimal
Count how many spaces you moved the decimal- if you moved right the exponent is negative and if you moved left it is positive
Get rid of any nonsignificant digits (more on this later)
Write the number multiplied by 10 to the power of however many spaces you moved in step 2

20. Practice Problems
1. Write the following numbers in scientific notation.
1.156
21.8
0.0068
27.635
0.219
444
2. Write out the following numbers in full with the correct number of zeroes.
8.69x104
9.1x103
8.8x10-1

21. Scientific Notation and Calculators
On your calculator, scientific notation is often shown using the letter “E”
So 9.2 x 10-4 would be written 9.2 E -4
To enter a number look for the EE or Exp key

22. Try it on your calculator
To check yourself, multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer should be 2.4 x 109.

23. Accuracy and Precision
No measurement is perfectly exact!

24. Precision Degree of exactness Written as +n ex: 40.1+1mm
Increase precision by finer divisions of the scale
This meter stick has divisions down to the mm so you can be precise to 0.5mm

25. Accuracy Are your measurements correct?
Calibration checks measuring tools against a standard

26. Significant Digits Valid digits in a measurement
Depends on the scale used
Using top ruler, we are certain of 2.5 and are guessing 2.55 so 2 sig digs
Using the bottom ruler we are certain of 2 and are guessing 2.5 so 1 sig dig

27. Sig Digs What if your measurement falls exactly on the line of 2.5mm?
Record it as 2.50mm because you are certain to within 0.01mm

28. Sig Digs: the rules Nonzero digits always sig
Final zeros after a decimal pt always sig
Zeros btwn other sigs are always sig
Final zeros that are not after a decimal pt are unknown-
3400 could have 2,3,or 4 sig digs
Write it in scientific notation to clarify

29. Working with Sig Digs
RESULTS NEVER HAVE MORE SIG DIGS THAN YOU STARTED WITH
Do the math first:
Add/subtract: perform operation and then round to lowest decimal sig figs that you started with
Multiply/divide: perform operation and then round to lowest total sig figs that you started with
Write 4 numbers on a piece of paper and trade it with your neighbor- decide how many sig digs

30. The bottom line on sig digs:
Don’t write out everything your calculator displays!!! Your answer should only include the sig digs.

31. Review You have 2 measurements: A=1.24m and B=0.23cm
Which has more sig digs?
Which is more precise?

32. Review
You put your backpack on a scale and find that it weighs 14.2kg. What is the range of weights implied by this measurement? How would you write that?
kg (1/2 of the smallest division of measurement)

33. Graphs Remember the basics of experiments?
Independent variable is manipulated
Dependent variables change as a result
Graph independent vs dependent

34. Linear relationships y=mx+b Slope=m= y/ x
Remember + slope is up to the right,
-slope is down to the right

35. Nonlinear relationships
Quadratic- when one variable depends on the square of another- y=ax2+bx+c
Inverse- when y variable depends on 1/x

36. Practice: graphs
Practice problems p. 18 # 24