1. Measurements
We need numbers in order to accurately take measurements
When executing the scientific method we must perform experiments  measurements  data
Express measurements using units
International System of Units (SI) aka: Metric system (meters, grams, seconds)
English units (feet, slugs, seconds)
Unfortunately American students must learn both systems!
Units allow us to describe things numerically
Measurement standards – a fixed and reproducible value for the purpose of taking accurate measurements

2. How do we know the length of a meter, yard?
Egyptians, cubit
King Louis XIV, foot
Distance from equator to north pole
1/10,000,000, meter, from Greek metron for “measure”
Modern standard, distance light,travels
in 1/299,792,458 s
Distance from Earth to nearest m
large galaxy
One light year m
Radius of Earth m
Height of person 2 m
Diameter of a period in a sentence 10-4 m
Diameter of a hydrogen atom m
Diameter of a proton m

3. Mass is the amount of matter an object contains – different than,
The mass of things
Mass is the amount of matter an object contains – different than,
something's weight!
Mass is measured in kilograms, grams, milligrams, etc…
How do we know the mass of a kilogram? – the kilogram is defined to
be the mass of a cylinder of platinum-iridium kept at the
international Bureau of Weights and Measures
Quart of milk ~ 1 kg
Typical Masses
Milk Way Galaxy
4  kg
Earth
6  kg
Space Shuttle
2  10 6 kg
Elephant
5400 kg
Automobile
1200 kg
Human
70 kg
Baseball
0.15 kg
Honeybee
1.5  10 –4 kg
Bacteria
10 –15 kg
Hydrogen Atom
1.67  10 –27 kg
Electron
9.11  10 –31 kg

4. - originally defined in terms of a fraction of the average day
The time of things
Define time? Even though we all have a sense of what time is, it’s difficult to give a good definition for it.
In scientific work we need to know: When did it happen? How long did it take?
How do we know the time of a second?
- originally defined in terms of a fraction of the average day
(1 second = 1/86,400 of an average day)
- currently defined in terms of the frequency of radiation emitted from a cesium atom (called an atomic clock)
Typical Times
Age of the universe
5  s
Age of the Earth
1.3  s
Existence of Humans
6  s
Human Lifetime
2  10 9 s
One Year
3  10 7 s
One Day
8.6  10 4 s
Time between heartbeats
0.8 s
Human reaction time
0.1 s
One cycle of an AM radio wave
10 –6 s
One cycle of a visible light wave
10 –15 s

5. Converting Units of Measurement – Dimensional Analysis
It is often the case that we must convert from one set of units to another.
Suppose we want to convert 316 ft to its equivalent in meters
these cancel !
Example: How many kilometers is 50,000 inches?
left with the units we
want !
The order that you apply the conversions makes no difference in the end!

6. Converting Units of Measurement – Dimensional Analysis
If I run 10 m/s in a school zone posted 20 miles/hour,
am I speeding? Here we must convert two things: meters to miles, and seconds
to hours
Conversions are a breeze with the metric system because it is based on powers
of 10!

7. Notice these powers match!
Converting Units of Measurement – Dimensional Analysis
Converting higher order units
If I have a house with 2,000 ft2 how many m2 does this correspond to?
1 m = 3.28 ft
Notice these powers match!

8. Prefix Power Examples Kilo- 1000, 103 Hecto- 100, 102 Deca- 10, 101
Converting Units of Measurement – Dimensional Analysis
Prefix
Power
Examples
Kilo-
1000, 103
Kilometer, Kiloliter, Kilogram
Hecto-
100, 102
Hectometer,Hectoliter,Hectogram
Deca-
10, 101
Decameter,Decaliter,Decagram
m, l, gr
1, 100
meter,liter,gram
Deci-
0.1, 10-1
Decimeter,Deciliter,Decigram
Centi-
0.01, 10-2
Centimeter,Centiliter,Centigram
Milli-
0.001, 10-3
Millimeter,Milliliter,Milligram
What if I had 10 milliliters and needed to convert this to kiloliters?
There’s a cooler way to do it and it involves my friend Hector!

9. Prefix Power Examples Kilo- 1000, 103 Hecto- 100, 102 Deca- 10, 101
Converting Units of Measurement – Dimensional Analysis
Prefix
Power
Examples
Kilo-
1000, 103
Kilometer, Kiloliter, Kilogram
Kind
Hecto-
100, 102
Hectometer,Hectoliter,Hectogram
Hector
Deca-
10, 101
Decameter,Decaliter,Decagram
Decked
m, l, gr
1, 100
meter,liter,gram
Mr.
Deci-
0.1, 10-1
Decimeter,Deciliter,Decigram
Deci
Centi-
0.01, 10-2
Centimeter,Centiliter,Centigram
Cinema
Milli-
0.001, 10-3
Millimeter,Milliliter,Milligram
Monday
Kind Hector Decked Mr. Deci at the Cinema on Monday.
K H D M D C M Each word represents one of the powers of ten in the
metric system!!

10. Converting Units of Measurement – Dimensional Analysis
K H D M D C M
So let’s look at how this works using the example we just did.
What if I had 10 milliliters and needed to convert this to kiloliters?
K H D M D C M
10.0 mL = ?? kL
K H D M D C M
Notice that I had to move over 6 letters to get to the “K” (or Kilo). So this corresponds to the number (and direction) of spaces I have to move my decimal!
10.0 mL = kL
Let’s try another example!

11. Converting Units of Measurement – Dimensional Analysis
We can use converting units to solve some neat problems.
How about this. If I know that a stack of 1,000 - $1 bills is = 1 inch in height
Could I jump over $1,000,000?
Where would we start?
???
If I could jump this high I would be in the NBA!!

12. 7-inch and 14-inch pizzas ($4.95, $13.95)
Look this stuff is even useful for everyday life!!
CAN YOU BELIEVE IT!!
7-inch and 14-inch pizzas ($4.95, $13.95)
How much bigger is the 14-inch and which is the better buy?
Area of a circle = r2
7-inch Area = inch inch Area = inch2
Best Buy? (Price per inch2)
7-inch $ 4.95/153.9 inch2 14-inch $ 13.95/615.7 inch2
0.03 $/inch $/inch2

13. Dimensional Analysis
Any valid physical formula must be dimensionally consistent – each term must have the same dimensions
From the table:
Distance = velocity × time
Velocity = acceleration × time
Energy = mass × (velocity)2