Units & Dimensions!

What we measure with!• Unit -

What we measure!

• Dimension -

• Fundamental dimensions - Basic, measurable characteristics which are not comprised of simpler or different dimensions.

• For our purposes, there are four fundamental dimensions:

Length MassTime Electric Charge

Units & Dimensions!

• Derived dimensions - More complex measurable characteristics which are comprised of combinations of simpler or different dimensions.

• Examples: Units Dimensions

Velocity – Miles length Hour time

Density – Mass mass Volume length x length x

length

Units & Dimensions!

• Unit Manipulation - This refers to the rules that govern how we use and combine units in calculations.

1. Like Units may be added and subtracted.

5 grams + 4 grams = 9 grams

2. Units of different dimensions cannot be added

or subtracted (this makes no sense).

5 grams + 4 seconds = ?????

Units & Dimensions!

3. Different Units for the same dimension may be added and subtracted, but must be converted to like units first.

5 grams + 4 kilograms = 5 grams + 4000 grams = 4005 g

4. Units of different dimensions may be multiplied and divided!

10 kilograms x 4 meters = 8 kg·m 5 seconds s