How to study physics: learn the principles, then a problem routine

For every equation, make sure you can say in words what it means and when it applies. $F = ma$ says that a resultant force makes an object accelerate, and that the same force gives a heavier object a smaller acceleration. If you can explain that, you'll also be able to answer the "explain" questions that carry many of the marks.

A quick test: cover your notes and explain each equation on your formula sheet to someone else, or out loud to yourself. The ones you can't explain are what to study next.

Use the same steps every time:

1. Sketch the situation.
2. List what you know and what you need, with units.
3. Choose the principle and the equation that links them.
4. Rearrange the equation before putting numbers in.
5. Substitute, with units.
6. Check: are the units right? Is the size sensible?

A ball is dropped from a height of 20 m. How fast is it moving just before it hits the ground? (Ignore air resistance; $g = 9.8\ \text{m/s}^2$.)

• Principle: conservation of energy. Gravitational potential energy becomes kinetic energy: $mgh = \tfrac{1}{2}mv^2$.
• Rearrange: the mass cancels, so $v = \sqrt{2gh}$.
• Substitute: $v = \sqrt{2 \times 9.8 \times 20} = \sqrt{392} \approx 19.8\ \text{m/s}$.
• Check: about 20 m/s for a fall of 20 m is reasonable, and the units are m/s.

Notice that the answer doesn't depend on the mass. Spotting results like that is part of understanding the physics, not just the maths.

Chi and colleagues' finding suggests a useful exercise. Take ten mixed problems and, before solving any of them, sort them into groups by principle: Newton's second law, conservation of energy, conservation of momentum, wave speed, and so on. Then solve them.

This trains the hardest skill in a physics exam: deciding which idea a question needs when it doesn't tell you. Mixing problem types during practice (rather than doing twenty of the same type in a row) builds the same skill; the Dunlosky review rated this kind of interleaved practice as moderately useful.

Many lost marks come from units and algebra, not physics:

• Convert to standard units first: km to m, g to kg, minutes to seconds, km/h to m/s (divide by 3.6).
• Rearrange before substituting. From $V = IR$, a 12 V supply and a current of 0.5 A give $R = \dfrac{V}{I} = \dfrac{12}{0.5} = 24\ \Omega$.
• Keep units in your working; if they don't simplify to the unit you expect, something is wrong.

Graphs are physics in a picture. Know what the gradient and the area mean for the graphs in your course:

Practise describing a graph in words ("constant acceleration, then constant speed") as well as calculating from it.

Practice testing and spreading study over time were rated the most useful study techniques in a large review of the research (Dunlosky et al., 2013). In physics, that means doing problems without notes, checking them, and coming back to older topics every few days. Keep a mistakes log, recording what went wrong (wrong principle, units, algebra or arithmetic), and redo those problems later.

If a problem has you stuck for more than about ten minutes, find the specific step you can't do and ask about it. TutorAura's AI physics tutor asks you to make each move yourself ("what do you know, and what do you need?") so you learn the routine rather than copy an answer.