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what are dimensions?

hi

there are fundamental physical quantities such as length, time, mass, etc and there are derived physical quantities such as speed, area etc. My teacher keeps repeating the word 'dimensions' over and over and I'm confused with quantities and dimensions.

Could someone explain clearly the difference between the two?
Dimensions have 2 meanings. One of the meanings means the length of a side or geometric values of a shape e.g. radius, length, area etc. The other one means how many directions something can move in. We live in a 3-dimensional world but your computer screen is only 2-dimensional. A quantity is a value. e.g. A cube will have dimensions of the same value. If the cube had one side 3cm the dimensions would be 3cm by 3cm by 3cm. Length is a quanity so you could say the cube has sides 3cm.

Hope this helps.
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Pangol
15
Original post by nichu
hi

there are fundamental physical quantities such as length, time, mass, etc and there are derived physical quantities such as speed, area etc. My teacher keeps repeating the word 'dimensions' over and over and I'm confused with quantities and dimensions.

Could someone explain clearly the difference between the two?

As you say, a quantity is a "thing" such as length, time, mass. etc. Let's stick with length as an example. The quantity is length, but how should we measure it? There are lots of possibilities - we could use metres, miles, inches, centimetres, light years, etc. All of these are dimensions of length, that is, ways of measuring length using some system of units. Which one we decide to use doesn't really matter, but the quanitiy length will be measured using a unit which is a dimension of length.

Now let's consider speed. We have the quantity speed, easily understood as how fast something is moving. We would measure this using a unit such as m s-1 or miles per hour - in both cases, what we have is the dimension of length divided by the dimension of time. The actual choice of unit again doesn't matter, but it will always be measured in some sort of length divided by some sort of time.

One of the nice things about this is that you can check if an equation makes sense by comparing the dimensions of both sides and seeing if they are the same or not. All valid equaitons must be dimensionally consistent. This doesn't tend to feature on Physics A Level specs, but it is part of some of the more advanced Mechanics units in the Further Maths A Level.
Hi,
As Pangol has described in detail, the dimensions of any measurement or parameter can be expressed atomically (in the simplest form) by three fundamental moieties: length, mass and time.

These are abbreviated to L, M and T.

So the dimensions of velocity are LT^-1

The dimensions of volume of liquid are L^3

OR of density: ML^-3

OR pressure (since pressure = force/area and force = mass X acceleration) :- M X LT^-2/L^2 = ML^-1T^-2

This is the formal method of quoting dimensions.
(edited 6 years ago)

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