Subject of formula : The basics

Subject of formula is a very important concept in physics since it will enable you to manipulate equations properly.

If you have the equation

s = ut + 0.5 at²

and you want to calculate the  acceleration a, how will you do it?

You will have to write an equation of a in term of the other quantities like

a =    

You will do this by moving the different quantities around until only a is left on one side. This is called making a the subject of formula.

We will start by studying four simple rules and then I will teach you how to use them to manipulate simple equations.

Rule 1

If you have the equation A + B = C and you want to have A in term of B and C what will you do?

A + B = C

You want A to remain on  the left-hand side, as a result you will want to move + B to the right-hand side.

The + B will have to change to – B when transferred to the right-hand side.

Hence A + B  = C

becomes

A = C - B 

The first rule is that a + on one side becomes a + on the other side.

Rule 2

If you have A – B = C and you want to have A in term of B and C what will you do ?

A – B = C

You want A to remain on the left-hand side and move – B to the right-hand side.

The – B will have to change to + B when transferred to the right-hand side.

Hence  A – B = C

becomes

A = C +B

The second rule is that a – on one side becomes a + on the other side. 

Rule 3

If you have A*B = C and you want to write A in term of B and C what would you do?

A*B = C 

If you want A to remain on the left-hand side then you would have to move *B to the other side.

The *B will have to change to /B when transferred to the right-hand side.

Hence A*B = C

becomes

A = C/B

The third rule is that a * on one side becomes a / on the other side.

Rule 4

If you have A/B = C and  you want to write A in term of B and C what would you do?

A/B = C

If you want A to remain on the left-hand side you will have to move /B to the other side.

The /B will have to change to *B when transferred to the other side.

Hence A/B =C

becomes

A = C*B

The fourth rule is that a / on one side becomes a * on the other side.