# Dimensions (involving units)

I need to work out to dimensions that are derived from their fundamental units..... I am having a small amount of trouble working out exactly how to do this....
eg: Force
Pressure
Energy (using W.D.= force x distance)

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Personally, I am not overly confident that I understand what you are asking for. Are you asking how to derive formulae or how they were formed?

P.S. I guess someone else will understand immediately but I am afraid I do not.

I think I know what Noxman wants.

You can derive any particular thing such as Energy and Pressure etc in fundamental units. The key is just to break them down. For example.

For Energy we know that W.D = F * d

d is distance measured in meters.

Force is measured in Newtons but this is not a fundamental unit....

So:

F = m * a

m is in Kg and a is acceleration and so in units of $$ms^-2$$

So units of W.D. => Energy or Joules = [Kg] [ $$m^2s^-2$$ ]

this should put you on the right track to do pressure by yourself. Last edited:
mukundpa
Homework Helper
F=ma
gives dimensions of F
[F] = [M] [M^0 LT^-2] = [M L T^-2]

hence W = F . s gives
[W] = [M L T^-2] [L] = [M L^2 T^-2]
do you want this??

HallsofIvy
Homework Helper
The "fundamental" units are: length, mass, time, charge, etc. Other units are "manufactured" from them as others have indicated:
velocity= distance/time,
acceleration= distance/time2, etc.

In the MKS system, we measure length in meters, mass in kg., time in seconds so the "unit" of speed is m/s, acceleration m/s2 (which have no separate name), force (from F= ma) kg-m/s2 (the "Newton"), energy (from either KE= (1/2)mv2 or work= distance*force) kg-m2/s2 (the Joule).

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Thankyou all for your help.... Everything is good now, rather annoyingly my teacher was doing it just because it had appeared on an exam like once in 20 years... Thankyou again.