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How to Rearrange Equations for GCSE Physics
How to Rearrange Equations for GCSE Physics
When approaching calculations you should follow the 7 Step Method. During step 3 you select the equation you need. However, sometimes you will need to rearrange the equation before you can use it.
Rearranging an equation is also called changing the subject of an equation. The subject is the variable you want to find and have on its own on one side of the equals sign.
In this article we will look at two methods for rearranging GCSE Physics equations: the equation triangle and algebra.
Contents
The Equation Triangle - Multiplication
The Equation Triangle - Multiplication
The equation triangle is a useful tool for quickly rearranging simple equations. It is easy to use and can be a shortcut when you are working with variables that are multiplying or dividing.
However, equation triangles cannot be used for every equation. If an equation involves addition, subtraction or more complicated mathematical operations, you will need to use algebra.
Let's take a quick look at the equation triangle before we have a more detailed look at algebra.
If an equation contains variables which are multiplying together, the multiplying variables are placed at the bottom of the equation triangle and the other variable is placed at the top.
For example:
F = m × a
The multiplying variables, m and a, are placed at the bottom of the triangle, while F is placed at the top.
If I want to rearrange the equation for m, I simply cover up the m. I am left with F over a.
Therefore:
m = F / a
Similarly, if I want to rearrange the equation for a, I cover up a and am left with F over m.
Therefore:
a = F / m
Try it now!
Place the equation P = I × V into an equation triangle and rearrange it for I and then rearrange it for V.
The Equation Triangle - Dividing
The Equation Triangle - Dividing
If you have an equation where variables are dividing, the variable above the division line goes at the top of the equation triangle. The other two variables are placed at the bottom of the triangle.
For example:
v = s / t
The variable s goes at the top, while v and t go at the bottom.
If I want to rearrange the equation for s, I cover up s and am left with v next to t. This means they are multiplying.
Therefore:
s = v × t
If I want to find t, I cover it up and am left with s over v.
Therefore:
t = s / v
Try it now!
Place the equation ρ = m / V into an equation triangle and rearrange it for m and then rearrange it for V.
Algebra - Multiplication
Algebra - Multiplication
Algebra can be used to rearrange all equations and should therefore be the method you aim to master.
You must get the variable you are looking for on its own. To do this, follow a very simple rule:
Do the opposite to the opposite side.
So what does this mean?
If I have the equation:
V = I × R
and want R to be the subject, R is currently being multiplied by I.
The opposite of multiplying is dividing.
So what do I divide by I?
The opposite side.
This gives:
R = V / I
I have done the opposite to the opposite side.
If I wanted to make I the subject, I is also being multiplied by R. The opposite of multiplying is dividing, so I divide the opposite side by R:
I = V / R
Try it now!
Rearrange the equation Q = I × t for t and for I using algebra.
Algebra - Dividing
Algebra - Dividing
Now let's look at an equation where variables are dividing.
If I have the equation:
P = E / t
and want to rearrange it for E, E is currently being divided by t.
The opposite of dividing is multiplying, so I must multiply the opposite side by t.
Therefore:
E = P × t
It can get a bit trickier if you need to rearrange the equation P = E / t for t.
First, rearrange the equation for E as we did above:
E = P × t
We now need to rearrange this new equation for t.
To make t the subject, I need to do the opposite of multiplying by P to the opposite side. I therefore divide by E by P:
t = E / P
Try it now!
Rearrange the equation P = F / A for F and for A using algebra.
Algebra - Addition and Subtraction
Algebra - Addition and Subtraction
The reason algebra is superior to the equation triangle is because you can also use it for equations involving addition and subtraction.
For example:
v² − u² = 2 × a × s
If I want to make v the subject, I must first remove u².
It is currently being subtracted from v², so I do the opposite to the opposite side and add u²:
v² = 2 × a × s + u²
I now need to get rid of the square on v.
The opposite of squaring is square rooting, so I must square root the opposite side:
v = √(2 × a × s + u²)
This is something an equation triangle cannot do, but algebra can.
Try it now!
Rearrange the equation v² − u² = 2 × a × s for u, a and s.
Common mistakes when rearranging equations
Common mistakes when rearranging equations
Rearranging equations can become much easier once you get used to the process, but there are some common mistakes to watch out for.
Rearranging for the wrong variable
Make sure you read the question carefully and identify which variable you need to find. It is easy to rearrange an equation correctly but make the wrong variable the subject.
Forgetting the final step
If your variable is squared, remember that you will need to square root at the end. Don't stop when you have found v² if the question asks you to find v.
Using an equation triangle when it won't work
Equation triangles are useful shortcuts, but they cannot handle equations involving addition or subtraction. When in doubt, use algebra.
Not checking your rearrangement
Once you have rearranged an equation, take a moment to check that it makes sense. You can substitute some simple values into both the original equation and your rearranged equation to see if they give the same result.
This is similar to step 7 of the 7 Step Method: Does your answer make sense? Don't blindly accept your rearrangement, instead check it.
For more GCSE Physics exam mistakes to avoid, take a look at my article 7 Common GCSE Physics Exam Mistakes (And How to Avoid Them).
Try it now!
Answer the following:
Why can't an equation triangle be used to rearrange v² − u² = 2 × a × s ?
Final Thoughts
Final Thoughts
So, can you use equation triangles for GCSE Physics?
Yes.
They are a useful shortcut for many of the simple equations you will come across. However, you should not rely on them for every equation.
Algebra is the method you should aim to master because it can be used to rearrange much more complicated equations.
If you are planning to study A-level Physics, mastering algebra now will also make your life much easier. The equations become more complicated and you will need to be confident rearranging them without relying on equation triangles.
So, by all means use equation triangles when they make a simple equation quicker to rearrange, but make sure you understand how to use algebra too.
Where next?
Are you finding revision boring? Here are 5 Fun and Effective Ways to Revise GCSE Physics.
Ready for a Different Kind of GCSE Physics Revision?
Ready for a Different Kind of GCSE Physics Revision?
Step inside an abandoned nuclear research facility in Atomic Pathways, the first adventure in An Interactive Physics Journey.
Use your GCSE Physics knowledge to solve problems, make decisions and survive the adventure. Every choice matters - and your mistakes will cost you Health Points!
Can you reach the end and earn the rank of Statistically Improbable Nuclear Physicist?
“It works incredibly well once you get into the story. It's also nice to see the information that goes beyond the usual GCSE specification, and it will certainly help students who engage with it.”
Lewis - Physics Online
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