Intro to
Physics
Scientific notation
Scientific notation is a system that makes it easy to work with the
huge range of numbers needed to describe the physical world.
Even very large or very small numbers can be simply expressed
as a coefficient multiplied by a power of ten.
Scientific notation
Scientific notation is a system that makes it easy to work with the
huge range of numbers needed to describe the physical world.
The coefficient is a
decimal number
between 1 and 10.
Scientific notation
Scientific notation is a system that makes it easy to work with the
huge range of numbers needed to describe the physical world.
The coefficient is a
decimal number
between 1 and 10.
Powers of ten are 10,
102 = 100, 103 = 1000,
104 = 10,000 and so on.
Numbers less than one
For numbers less than one, scientific notation uses
negative exponents:
The number 0.0015 is 1.5 ÷ 1000 = 1.5 × 10-3
Powers of ten
Powers of ten on a calculator
Calculators and computers use the symbol E or EE for powers of ten.
The letter E stands for “exponential” (another term for scientific notation).
Practice…
Use the calculator to write
numbers in scientific notation:
0.035
-2
3.5
a) 4,180 joules
4.18 x 103 joules (4.18 E3)
3.5 E-2
b) 0.035 meters
3.5 e-2
3.5 x
10-2
meters (3.5 E-2)
3.5 ee-2
Assessment
1. Express the following numbers in scientific notation:
a. 275
b. 0.00173
c. 93,422
d. 0.000018
Assessment
1. Express the following numbers in scientific notation:
a. 275
2.75 x 102
b. 0.00173
1.73 x 10-3
c. 93,422
9.3422 x 104
d. 0.000018
1.8 x 10-5
Importance of Units
In Physics units are a key to telling you what sort of quantity you’re
dealing with.
Having the units we use memorized will be vital to your success this
year!
Unless you’re told otherwise EVERY answer you have this year should
have UNITS with it! Units are like clothes for your #’s, we do NOT want
any naked #’s!
• Example You calculate that a ball traveled a distance of 5 meters.
• WRONG way to record answer  5
• RIGHT way to record answer  5m or 5 meters
The International System of Units
Measuring mass
In the SI system, mass has units of grams (g) and kilograms (kg).
One kilogram is 1000 grams.
Length
Length is a fundamental quantity.
There are two common systems of
length units you should know:
• The English system uses inches (in),
feet (ft) and yards (yd).
• The metric system using millimeters
(mm), centimeters (cm), meters (m),
and kilometers (km).
The meter is the SI base unit for length.
Surface area
Area is a derived quantity based on length. Surface area describes
how many square units it takes to cover a surface.
All surface area units are units of length squared (for example: m2).
Volume
Volume is another derived quantity based on length. It measures
the amount of space, in units of length cubed. (example: m3)
Density
Density is an example of a derived quantity. It measures the
concentration of mass in an object’s volume.
The symbol for density is this Greek letter, rho:
ρ
Density Tower - video
Why did the tower make layers and not mix together?
Solving for Density
A delivery package has a
mass of 2700 kg and a
volume of 35 cubic meters.
What is its density?
77 kg/m3
Calculating density
When calculating derived quantities, it will be important to use
consistent SI units.
For example: If density in kilograms per cubic meter is desired,
then the mass must be in kilograms, and the volume must be in
cubic meters.
Time
Time is a fundamental quantity. The SI unit of time is the second.
Converting units
When solving physics problems, the units you use must be consistent.
You need to be able to convert units to make them consistent.
To convert a quantity from one unit to
another, multiply by a conversion factor.
A conversion factor always has the value
of one (1) whether it is right-side-up or
upside-down.
Converting units
Here are some examples of
conversion factors for length.
Converting other units
To convert from one unit to another, multiply by the
appropriate conversion factor.
Pick the conversion factor that lets you cancel the unit
you don’t want, and end up with the unit you want.
• You’ll always “cancel” things diagonally
Test your knowledge
Use the conversion factor shown at right to
convert 12 inches to centimeters.
Test your knowledge
Use the conversion factor shown at right to
convert 12 inches to centimeters.
Flipping the conversion factor upside down lets you cancel
the unit you don’t want, and end up with the unit you want.
Converting Fractions
•
•
•
Converting values in fractions is a little different
Ex 1: Convert 10m/s to cm/s.
Ex 2: Convert 10m/s to m/hr.
Example 1
•
Convert 10m/s to cm/s.
Example 2
•
Convert 10m/s to m/hr.
Double conversions
•
Convert 10mi/hr (i.e. mph) to m/s
Assessment
1. Which of the following unit conversions is correct?
A.
B.
C.
Assessment
1. Which of the following unit conversions is correct?
A.
B.
C.
If this is a final answer, round to the correct number of significant figures.
Solving for a variable
Suppose this is the formula:
But the variable you are asked for is time t.
Solving for a variable
Solve the relationship for time, t :
Multiply both sides by 2:
(To get rid of a fraction you “flip & multiply”)
Solving for a variable
Solve the relationship for time, t :
Multiply both sides by 2:
(To get rid of a fraction you “flip & multiply”)
Divide both sides by a:
Solving for a variable
Solve the relationship for time, t :
Multiply both sides by 2:
Divide both sides by a:
Solving for a variable
Solve the relationship for time, t :
Multiply both sides by 2:
Divide both sides by a:
Take the square root of both sides:
(Square root will get rid of a square)
Solving for a variable
Solve the relationship for time, t :
Multiply both sides by 2:
Divide both sides by a:
Take the square root of both sides:
(Square root will get rid of a square)