Units in Equations
Here are some common Units:
And we put Metric Number Prefixes in front of the symbol to write larger or smaller values:
|billionth||0.000 000 001||nano||n|
|trillionth||0.000 000 000 001||pico||p|
- 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 "/"
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?
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