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What are Dimensions ?

For example, consider water in the beaker shown here:

Can be calculated or derived by multiplying or dividing fundamental dimensions.
Exampls: area, velocity, density and volume

2. Derived Dimensions -

Mass, Length, Time, Temperature, Moles and sometimes Force
Fundamental dimensions can be directly measured or are independently defined.
All other dimensions can be obtained from the fundamental dimensions.

1. Fundamental Dimensions -

There are two types of dimensions.

In science and engineering, numbers without units are not
useful (unless they happen to be dimensionless).

Mass

Density

has derived dimensions made up of a combination of fundamental dimensions:

is a fundamental dimension.

Lesson 1B: page 1 of 14

Previous LESSON

If I told you that I weighed 175, would you be worried that I might step on your foot ?
I guess that depends on whether I weighed 175 pounds, 175 kg or 175 tons, doesn’t it ?
Well, in science and engineering, a number without units like pounds or kg or ft/sec is just about meaningless.
The exception is that some quantities are dimensionless, but we won’t run into many of them in this course.
So, what is a dimension anyway ?
A dimension is a TYPE of unit.
Mass, length, time, temperature and sometimes force are fundamental dimensions.
Mass might have units of pounds, kg or tons.
Fundamental Dimensions cannot be reduced in terms of any combination of other fundamental dimensions.
For example, no combination of length, time and temperature is equivalent to mass.
Density is NOT a fundamental dimension because it is equivalent to mass over volume and volume is equivalent to length cubed.
So, density has dimensions of mass per length cubed. Because the dimensions of density can be written in terms of other fundamental dimensions, density is NOT a fundamental dimension.
Now, lets take a closer look at UNITS.

What are Dimensions ?

Ch1, Lesson B, Page 1 - What are Dimensions ?