Introduction to Physics Equations

Physics is often called the "study of how things work," and equations are the tools we use to describe those workings with precision. In your AQA GCSE Physics exam, you won't just be asked to define terms; you will need to use math to predict what happens in the real world.

This chapter focuses on a vital part of Working Scientifically: knowing which equations you must memorize (recall) and which ones you will find on the provided equation sheet (selection). Don't worry if you find the math side of Physics a bit scary at first—once you learn the patterns, it becomes much easier!

The Two Types of Equations

For your exams in 2027 and 2028, the rules are very specific:

  1. Recall Equations: These are formulas you must have memorized. They will not be given to you in the question.
  2. Selection Equations: These are provided on an equation sheet (insert). You need to be able to pick the right one for the problem and use it correctly.

Quick Tip: Even if an equation is on the sheet, you still need to know what each symbol stands for and what units to use!

Equations You Must Recall

These are the core formulas used across Paper 1 and Paper 2. We’ve grouped them by topic to help you learn them.

1. Forces and Motion

Weight: \(W = m g\)
(Weight = mass \(\times\) gravitational field strength)

Work Done: \(W = F s\)
(Work done = force \(\times\) distance moved along the line of action of the force)

Force applied to a spring: \(F = k e\)
(Force = spring constant \(\times\) extension)

Distance travelled: \(s = v t\)
(Distance = speed \(\times\) time)

Acceleration: \(a = \frac{\Delta v}{t}\)
(Acceleration = change in velocity \(\div\) time taken)

Resultant Force (Newton’s 2nd Law): \(F = m a\)
(Force = mass \(\times\) acceleration)

Momentum (Higher Tier Only): \(p = m v\)
(Momentum = mass \(\times\) velocity)

2. Energy and Power

Kinetic Energy: \(E_k = \frac{1}{2} m v^2\)
(Kinetic energy = \(0.5 \times\) mass \(\times\) speed squared)

Gravitational Potential Energy: \(E_p = m g h\)
(GPE = mass \(\times\) gravitational field strength \(\times\) height)

Power (Energy): \(P = \frac{E}{t}\)
(Power = energy transferred \(\div\) time)

Power (Work): \(P = \frac{W}{t}\)
(Power = work done \(\div\) time)

Efficiency: \(\text{efficiency} = \frac{\text{useful output energy transfer}}{\text{total input energy transfer}}\)
(You can also use Power in place of Energy for this formula).

3. Electricity

Charge Flow: \(Q = I t\)
(Charge = current \(\times\) time)

Potential Difference (Ohm’s Law): \(V = I R\)
(Voltage = current \(\times\) resistance)

Electrical Power: \(P = V I\) or \(P = I^2 R\)

Energy Transferred: \(E = P t\) or \(E = Q V\)

4. Other Key Recalls

Wave Speed: \(v = f \lambda\)
(Wave speed = frequency \(\times\) wavelength)

Density: \(\rho = \frac{m}{V}\)
(Density = mass \(\div\) volume)

Pressure: \(p = \frac{F}{A}\)
(Pressure = force normal to a surface \(\div\) area)

Key Takeaway: Memorizing these is like learning the vocabulary of a new language. Use flashcards to test yourself regularly!

Equations to Select (The Equation Sheet)

In the exam, you will have a sheet containing more complex equations. Your job is to select the right one based on the information given in the question.

Examples of equations on the sheet:

  • Elastic Potential Energy: \(E_e = \frac{1}{2} k e^2\)
  • Change in Thermal Energy: \(\Delta E = m c \Delta \theta\)
  • Period of a Wave: \(\text{period} = \frac{1}{\text{frequency}}\)
  • Magnification: \(\text{magnification} = \frac{\text{image height}}{\text{object height}}\)
  • (HT Only) Pressure in a liquid: \(p = h \rho g\)
  • (HT Only) Force on a conductor: \(F = B I l\)

How to Use Equations Step-by-Step

When you see a calculation question, don't panic! Follow the "FIFA" method to ensure you get maximum marks, even if you make a mistake at the end.

1. Formula: Write down the equation you are going to use. If it’s a recall equation, write it from memory. If it’s a selection equation, copy it from the sheet.

2. Insert: Put the numbers from the question into the formula exactly where they belong. This is called substitution.

3. Fine-tune: If the unknown value isn't the "subject" (the bit on its own before the equals sign), rearrange the equation now.

4. Answer: Calculate the final number and add the correct unit (e.g., \(J\) for Joules, \(W\) for Watts).

Example: A \(2kg\) mass moves at \(3m/s\). Calculate kinetic energy.
Formula: \(E_k = \frac{1}{2} m v^2\)
Insert: \(E_k = 0.5 \times 2 \times 3^2\)
Answer: \(9 J\)

Common Pitfalls to Avoid

  • Units: Always check if units need converting. Time must be in seconds (s), mass in kilograms (kg), and distance in meters (m). If a question gives you "minutes" or "grams," convert them first!
  • Squaring: In equations like \(E_k = \frac{1}{2} m v^2\), remember that only the velocity (\(v\)) is squared, not the whole side.
  • Significant Figures: Give your answer to the same number of significant figures as the values provided in the question (usually 2 or 3).

Quick Review: Working Scientifically

Equations aren't just for math marks. They help you with:

  • Predicting: If you increase the mass in \(F = ma\), and the force stays the same, you can predict the acceleration will decrease.
  • Graphing: Many equations follow the linear format \(y = mx + c\). For example, in \(V = IR\), if you plot \(V\) against \(I\), the gradient of the line is the resistance \(R\).

Did you know? The Greek letter delta (\(\Delta\)) just means "change in." So \(\Delta v\) is just the final speed minus the starting speed!

Key Takeaway: Success in Physics equations comes down to identifying what you know, selecting the right tool, and checking your units at the end.