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## Saturday, September 5, 2009

### Derived units

As we have seen in the last post there are 7 fundamental base units. From these 7 fundamental base units all the other units can be derived.

In fact if a quantity is not a basic quantity then it must certainly be a derived quantity and its unit a derived unit. The derived unit is based on one or more of the 8 fundamental base units. You must keep in mind that some quantities have units of their own based on famous scientists such as Joule (J) for energy or Newton (N) for force. For such quantities the unit can be used or the derived unit can be used.

We are now going to see several derived quantities and their derived units and how these derived units are obtained.

We are now going to see how these derived units are obtained. Once you know how to determine the derived units of common quantities like volume, force, etc then later on you will be able to determine the derived quantity for any other quantity.

So what is the method to obtain the derived unit of a quantity?

Example 1

We are going to start with a simple one: the derived unit for volume.

In order to deduce the derived unit of a quantity you need a formula to calculate the quantity. The formula must contain that you know the units in term of based unit.

Volume = length * width * height

Unit of [volume] = unit of [length * width * height]
= unit of [length] * unit of [width] * unit of [height]
= m * m *m
= m3

Example 2

What is the derived unit for acceleration?

In order to deduce the derived unit for acceleration, you must know a formula to calculate acceleration such as

Acceleration = velocity / time

The formula must contain quantities that you know the units in term of base units.

If in the new formula, there is quantity that you do not know the derived unit then you will also have to know the formula to calculate that quantity.

Velocity = displacement / time

You can now rewrite the formula for acceleration to

Acceleration = velocity / time
= (displacement / time) /time

So

the unit of acceleration = unit of [velocity / time]
= unit of [(displacement / time) /time]
= unit of [(displacement / time)] / unit of time
= (m/s) /s
= m *s-1 * s-1
= m s-2

Was it easy?

Now let us have a look at another example to confirm your newly learned skills.

Example 3

What is the derived unit for pressure?

Have you worked it out?

Now you would remember that in order to find the derived unit you need to know a formula for the quantity in term of quantities that you already know the units.

Pressure = Force / surface are

Hence unit of pressure = unit of [force] / unit of [surface area]
= unit of [mass * acceleration] / unit of surface area]
= (kg * m/ s2)/m2
= (kg m * s-2 * m -2
= Kg m-1 s-2

Do the following questions and post the answers in the comment section. I will give the correct answers later on after a few of you have submitted your answers.

Find the derived units for the following quantities.

1. Work done
2. Kinetic energy
3. Volume
4. Density

As you progress through the course you will meet more quantities that you would be able to derive the units.

Good luck and see you next time.