1. Unit Systems and Dimensional Analysis

2. Units of measurement The Fundamental SI Units
Physical Quantity
Name of Unit
Abbreviation
Mass
kilogram kg
Length
meter m
Time
second s
Temperature
kelvin K
Electric current
ampere A
Amount of substance
mole
mol
Luminous intensity
candela cd
SI-derived Unit is an SI unit derived by combining two or more SI base units
E.g SI unit of speed.

3. Metric Unit of Mass The Kilogram (kg) Is the SI Unit of mass
Mass ≠ Weight
Mass is a measure of the total quantity of mater in an object. Mass does not vary.
Weight is the measure of force that gravity exerts on an object. Weight varies with the strength of the gravitational field.

4. Metric Unit of Volume
Area is a measure of the extent of a surface. Common units are sq. in. , sq.ft, sq.cm
Volume is a measure of amount os space occupied by an object. It is a three dimentional and thus involves units that have been cubed.

5. Conversion Factor
To convert from one unit to another, it is neccesary to use the equivalence statement that relates the two units.
A conversion factor is a ratio that specifies how one unit of measurement is related to another unit of measurement. Or simply relationship between two units.
1 min = 60 sec
1 gal = 4qt
1yd = 3ft

6. Dimensional Analysis
Arrange conversion factors so the starting unit cancels

7. Systematic Approach to Problem Solving
Sort the information from the problem
identify the given quantity and unit, the quantity and unit you want to find, any relationships implied in the problem
Design a strategy to solve the problem
devise a conceptual plan
sometimes may want to work backward
each step involves a conversion factor or equation
solve the problem
check that units cancel properly
multiply terms across the top and divide by each bottom term
Check the answer
double-check the set-up to ensure the unit at the end is the one you wished to find
check to see that the size of the number is reasonable
because centimeters are smaller than inches, converting inches to centimeters should result in a larger number

8. Example #1
A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?
(1ft =12in)
Example #2
An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams?
(1 kg = lbs; 1 kg = 1000 g)
1). 82

9. Density Mass of substance per unit volume of the substance.
Common units are g/cm3 or g/mL.

10. For equal volumes, denser object has larger mass
For equal masses, denser object has smaller volume
Heating an object generally causes it to expand, therefore the density changes with temperature

11. Example 1. 3: Decide if a ring with a mass of 3. 15 g that displaces 0
Example 1.3: Decide if a ring with a mass of 3.15 g that displaces cm3 of water is platinum
Write down the given quantities and the quantity you want to find
Given:
Find:
Equation:
mass = 3.15 g
volume = cm3
density, g/cm3
Find the equation that relates the given quantity to the quantity you want to find
Solve the equation for the quantity you want to find, check the units are correct, then substitute and compute
Compare to accepted value of the intensive property
Density of platinum = 21.4 g/cm3
therefore not platinum

12. Temperature Scales
Temperature is the measure of hotness or coldness of an object
Fahrenheit scale, °F
used in the U.S.
Celsius scale, °C
used in all other countries
Kelvin scale, K
0 K = absolute zero

13. Fahrenheit vs. Celsius
A Celsius degree is 1.8 times larger than a Fahrenheit degree
The standard used for 0° on the Fahrenheit scale is a lower temperature than the standard used for 0° on the Celsius scale

14. Kelvin vs. Celsius
The size of a “degree” on the Kelvin scale is the same as on the Celsius scale
The 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale

15. Example 1.2: Convert 40.00 °C into K and °F
Find the equation that relates the given quantity to the quantity you want to find
Given:
Find:
Equation:
40.00 °C K
K = °C
Because the equation is solved for the quantity you want to find, substitute and compute
K = °C
K =
K = K
Find the equation that relates the given quantity to the quantity you want to find
Given:
Find:
Equation:
40.00 °C °F
Solve the equation for the quantity you want to find
Substitute and compute

16. Common Prefix Multipliers in the SI System

17. Common Units and Their Equivalents
Length
1 kilometer (km) =
mile (mi)
1 meter (m)
39.37 inches (in.)
1.094 yards (yd)
1 foot (ft)
30.48 centimeters (cm)
1 inch (in.)
2.54 centimeters (cm) exactly

18. Common Units and Their Equivalents
Mass
1 kilogram (km) =
2.205 pounds (lb)
1 pound (lb)
grams (g)
1 ounce (oz)
28.35 grams (g)
Volume
1 liter (L) =
1000 milliliters (mL)
1000 cubic centimeters (cm3)
1.057 quarts (qt)
1 U.S. gallon (gal)
3.785 liters (L)