Units in Equations
Here are some common Units in Physics:
| Property | Name | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Force | Newton | N |
| Energy | Joule | J |
| Per second | Hertz | Hz |
And we put Metric Number Prefixes in front of the symbol to write larger or smaller values:
| Name | The Number | Prefix | Symbol |
| trillion | 1,000,000,000,000 | tera | T |
| billion | 1,000,000,000 | giga | G |
| million | 1,000,000 | mega | M |
| thousand | 1,000 | kilo | k |
| hundred | 100 | hecto | h |
| ten | 10 | deka | da |
| unit | 1 | ||
| tenth | 0.1 | deci | d |
| hundredth | 0.01 | centi | c |
| thousandth | 0.001 | milli | m |
| millionth | 0.000 001 | micro | µ |
| billionth | 0.000 000 001 | nano | n |
| trillionth | 0.000 000 000 001 | pico | p |
Examples:
- km: k for kilo, m for meter becomes kilometer (a thousand meters)
- mm: m for milli, m for meter becomes millimeter (a thousandth of a meter)
- MN: M for mega, N for Newton becomes meganewton (a million Newtons)
- g: g for gram, one symbol only is just the unit, so that is grams
- µs: µ for micro, s for second becomes microsecond (a millionth of a second)
Now ... how do we us them in equations?
First: it is common to just use the symbol (such as km for kilometers).
Adding and Subtracting
Use the same units when we add or subtract!
Example: Sam is designing a new table. The old table is 2 m long. The new table should be 200 mm longer:
2 m + 200 mm = ?
The units need to be the same!
We can choose m (meters) or mm (millimeters).
Let's choose mm. 1 m is 1000 mm, so:
2000 mm + 200 mm = 2200 mm
Or we could choose m:
2 m + 0.2 m = 2.2 m
Multiplying and Dividing
When multiplying put the units next to each other
When dividing put the unit after "/"
Like this:
Example: Alex walks 100 m in 80 seconds, what average speed is that?
Speed is distance/time
Speed = 100 m 80 s = 1.25 m/s
100 divided by 80 is 1.25, and m divided by s is m/s
Example: Hunter kicks a soccer ball. It goes from 0 to 32 m/s in 0.1 seconds. What is the acceleration?
Acceleration is:
Change in Velocity (m/s) Time (s)
Put in the values we know:
Acceleration = 32 m/s − 0 m/s 0.1s = 320 m/s2
The "m/s" becomes "m/s /s" which is m/s2
Sometimes there is a special unit that is made up of other units:
Example: The soccer ball weighs 0.4 kg, what is the force of Hunter's kick?
We can use Newton's Second Law of Motion:
F = ma
The mass m = 0.4kg,
and we already calculated the acceleration: a = 320 m/s2
F = 0.4 kg × 320 m/s2
F = 128 kg m/s2
1 Newton (N) is the usual measure of force, and equals 1 kg m/s2, so:
F = 128 N