Students will learn about the metric system and how to convert between metric units.
Frequently Used Measurements, Greek Letters, and Prefixes
Measurements
Type of measurement | Commonly used symbols | Fundamental units |
---|---|---|
length or position | meters (m) | |
time | seconds (s) | |
velocity or speed | meters per second (m/s) | |
mass | kilograms (kg) | |
force | Newtons (N) | |
energy | Joules (J) | |
power | Watts (W) | |
electric charge | Coulombs (C) | |
temperature | Kelvin (K) | |
electric current | Amperes (A) | |
electric field | Newtons per Coulomb (N/C) | |
magnetic field | Tesla (T) |
Prefixes
SI prefix | In Words | Factor |
---|---|---|
nano (n) | billionth | |
micro (µ) | millionth | |
milli (m) | thousandth | |
centi (c) | hundreth | |
deci (d) | tenth | |
deca (da) | ten | |
hecto (h) | hundred | |
kilo (k) | thousand | |
mega (M) | million | |
giga (G) | billion |
Greek Letters
“mu” | “tau” | “Phi”^{*} | “omega” | “rho” |
---|---|---|---|---|
“theta” | “pi ” | “Omega”^{*} | “lambda” | “Sigma”^{*} |
“alpha” | “beta” | “gamma” | “Delta”^{*} | “epsilon” |
Two very common Greek letters are and . is used to indicate that we should use the change or difference between the final and initial values of that specific variable. denotes the sum or net value of a variable.
- Every answer to a physics problem must include units. Even if a problem explicitly asks for a speed in meters per second (m/s), the answer is 5 m/s, not 5.
- If a unit is named after a person, it is capitalized. So you write “10 Newtons,” or “10 N,” but “10 meters,” or “10 m.”
- Metric units use a base numbering system of 10. Thus a centimeter is ten times larger than a millimeter. A decimeter is 10 times larger than a centimeter and a meter is 10 times larger than a decimeter. Thus a meter is 100 times larger than a centimeter and 1000 times larger than a millimeter. Going the other way, one can say that there are 100 cm contained in a meter.
Example 1
Question: Convert 2500 m/s into km/s
Solution: A km (kilometer) is 1000 times bigger than a meter. Thus, one simply divides by 1000 and arrives at 2.5 km/s
Example 2
Question: The lengths of the sides of a cube are doubling each second. At what rate is the volume increasing?
Solution:The cube side length, , is doubling every second. Therefore after 1 second it becomes . The volume of the first cube of side is . The volume of the second cube of side is . The ratio of the second volume to the first volume is . Thus the volume is increasing by a factor of 8 every second.
Watch this Explanation
Time for Practice
- A tortoise travels meters west, then another centimeters west. How many meters total has she walked?
- A tortoise, Bernard, starting at point A travels west and then millimeters east. How far west of point is Bernard after completing these two motions?
- . What is ?
- A square has sides of length . What is the area of the square in ?
- A square with area is stretched so that each side is now twice as long. What is the area of the square now? Include a sketch.
- A rectangular solid has a square face with sides in length, and a length of . What is the volume of the solid in ? Sketch the object, including the dimensions in your sketch.
- As you know, a cube with each side in length has a volume of . Each side of the cube is now doubled in length. What is the ratio of the new volume to the old volume? Why is this ratio not simply ? Include a sketch with dimensions.
- What is the ratio of the mass of the Earth to the mass of a single proton? (See equation sheet.)
- A spacecraft can travel . How many km can this spacecraft travel in 1 hour ?
Answers
- each side goes up by , so it will change by