Math and natural sciences

How to learn physics from scratch

For many people school physics stayed a pile of formulas to plug numbers into before a test. As an adult you have it easier: you can take your time and ask, every time, where a formula comes from and what it describes in the real world. The plan below goes from mechanics to electricity and optics — in the order in which each topic rests on the previous one.

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The math you need in advance#

For an introductory course, algebra is enough: rearranging a formula for one quantity, solving linear and quadratic equations, working with powers of ten. From geometry you need the right triangle, sine and cosine, because forces and velocities are split into components. Derivatives and integrals are not needed on the first pass; you will want them if you go on to university-level physics. If your algebra has faded, spend a month on it first — the plan in learn math from scratch covers exactly that — otherwise every physics problem will stall on the math rather than on the physics.

Mechanics: where everything starts#

Mechanics takes the first third of the plan, and that is justified: it is where you learn to think like a physicist. Start with kinematics — distance, velocity, acceleration, motion graphs. Then dynamics: Newton's three laws, gravity, friction, elastic forces. After that, momentum and energy and the conservation laws. Linger here: many problems that are hard to solve with forces take two lines with conservation of energy.

The sign that mechanics has sunk in: for any problem you can draw a free-body diagram of the forces acting on an object and explain why it moves the way it does.

Heat and the behaviour of gases#

Temperature, pressure, the gas laws, heat capacity, phase changes, the first law of thermodynamics. This topic maps well onto everyday experience: why a pressure cooker cooks faster, why windows fog up, where the heat from a kettle goes. Try to tie every concept to an example like that.

Electricity and magnetism#

Charge, electric field, voltage, current, resistance, Ohm's law, series and parallel circuits, power. Then the magnetic field and electromagnetic induction — how a generator and a transformer work. Free simulators where you can build a circuit and watch the current and voltage change are especially useful for electricity.

Oscillations, waves and optics#

The pendulum and the spring, sound, reflection and refraction of light, lenses. You can finish the first pass with an overview of what came after classical physics: the structure of the atom, the photoelectric effect, radioactivity — without heavy derivations, just enough to see where to go next.

How to solve physics problems#

Use one routine every time: write down what is given, in SI units; draw a diagram; choose the law; get the answer in general form (in letters); and only then substitute numbers. An answer in letters is easy to check by its units: if a velocity comes out in kilograms, you have found the mistake before calculating anything. The second trick is an estimate: is it plausible that a car reaches 100 km/h in half a second?

How to keep notes#

One page per topic: the main quantities with their units, two or three laws with a note on when they hold, and one fully worked problem. Keep a separate list of conditions: "neglect friction", "ideal gas", "speed much less than the speed of light". Those are what people usually forget. A notes method that suits this kind of material is described in how to take notes.

Common mistakes on the first pass#

  • Writing down formulas without the conditions they need. The distance formula for constant acceleration does not work if the acceleration changes.
  • Mixing up mass and weight, velocity and acceleration, energy and power. A small table of quantities helps: symbol, unit, what it describes.
  • Forgetting to convert units: kilometres per hour and grams in a problem almost always need to become metres per second and kilograms.
  • Reading worked solutions instead of solving. Recognising a solution is easy; coming up with it yourself is a different skill.

Step-by-step plan

  1. Month 1 — algebra and kinematicsRevise equations and right-triangle trigonometry; distance, velocity, acceleration, motion graphs.
  2. Months 2–3 — dynamics and conservation lawsNewton's laws, forces, momentum, energy; a free-body diagram for every problem.
  3. Month 4 — heatGas laws, heat capacity, phase changes, the first law of thermodynamics.
  4. Months 5–6 — electricity and magnetismOhm's law, circuits, power, the magnetic field, induction; experiments in a simulator.
  5. Month 7 — waves and opticsOscillations, sound, refraction and lenses; an overview of atomic physics.

Start learning this in your own space

The plan goes into your repository: tick off stages, keep notes — the change history shows how far you have come.

Start the plan

Check yourself

1.A car travels 120 km in 1.5 hours. What is its average speed in km/h?

2.A force gives a 2 kg object an acceleration of 3 m/s². What is the force in newtons?

3.The voltage across a resistor is 12 V and its resistance is 4 Ω. What current flows through it, in amperes?

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