Understanding Units: Calculations with Units

[tomtomtom1]

Homework Statement

Understanding Units

Relevant Equations

T = L^2

Hi

I am trying to figure understand what happens to the units when I perform calculations on them. For instance, given the equation:-

T = L^2

If the value of L was 78mm then what would the value of T be?

Would it be:

(78mm)^2 = 78^2 mm^2 = 6084mm^2

or would it be:-

(78mm)^2 = 78^2 = 6084mm

Can anyone shed any light?

Thank you.

 

[SammyS]

Problem Statement: Understanding Units
Relevant Equations: T = L^2

Hi

I am trying to figure understand what happens to the units when I perform calculations on them. For instance, given the equation:-

T = L^2

If the value of L was 78mm then what would the value of T be?

Would it be:

(78mm)^2 = 78^2 mm^2 = 6084mm^2

or would it be:-

(78mm)^2 = 78^2 = 6084mm

Can anyone shed any light?

Thank you.

You multiply the units as well as the numbers.

 

[phyzguy]

You should carry the units along and they get exactly the same arithmetic operations as the numerical values. So if L has units of mm, T will have units of mm^2.

 

[symbolipoint]

Your units that you write can become confusing, in this case to the extent of ambiguous.

If you are indicating the unit for L is the METER, which you could abbreviate as M, then your expression using variable R with including the unit, becomes (L)(L)(METER)(METER), as I here include the unit, and so T=L^2(METER)^2
and then the unit for T is METER².

 

[symbolipoint]

Note in post #4, I spelled the word because "m" looks like could be "meter" or later "mm" could be misread as "millimeters".