How to study first-year university physics

Why university physics feels harder than high school physics

In grade 12 you could often get through a test by matching a question to the formula that fit it. First-year courses in mechanics and electricity and magnetism are built to stop that working. Problems combine two ideas at once, give you more information than you need, or ask for an answer in symbols instead of a number. The math also steps up: vectors, a little calculus, and algebra with five letters in it.

The good news is that the course is smaller than it looks. A first term of mechanics rests on a handful of principles: kinematics, Newton's second law, work and energy, momentum, and rotation. The second-term E&M course adds Coulomb's law, electric fields and potential, circuits, and magnetic fields. Almost every problem is one of these principles applied carefully. Your job is to recognize which one, and to apply it without slips.

David Harrison's study notes for University of Toronto physics students make the same point: memorizing equations will not carry you, and the students who do well work steadily, form study groups, and do their own homework rather than copying solutions. If you are still in high school, the physics readiness deck is a quick check of the algebra, trigonometry and vector skills first year assumes.

A five-step method for physics problems

Physics education researchers at the University of Minnesota (Heller, Keith and Anderson, 1992) taught first-year students an explicit problem-solving strategy and had them practise it in small groups. The version below is a plain adaptation of that idea. It feels slow for the first two weeks. After that it becomes quick, and it is the habit that holds up under exam pressure.

1. Diagram. Sketch the situation. For forces, draw a free-body diagram for each object with every force as an arrow, labelled. Choose and mark your axes.
2. Knowns and unknown. List each given quantity with its symbol and units, converted to SI (metres, kilograms, seconds, coulombs). Write the unknown with a question mark.
3. Principle. Name the physics in words before writing an equation: "Newton's second law along the incline", "energy is conserved because there is no friction", "momentum is conserved in the collision".
4. Solve in symbols, then substitute. Rearrange for the unknown using letters only. Put numbers in at the last line, with units.
5. Check. Do the units come out right? Is the size reasonable? Does the expression behave sensibly if you set a mass, angle or friction coefficient to zero?

Worked examples in mechanics and E&M

Here are three typical first-year problems solved with the five steps. The numbers were checked by computer; we use g = 9.81 m/s², the value most first-year courses use.

Notice how often the check step does real work. In Example 2 it tells you the mass did not matter; in Example 3 it catches the most common unit slip in E&M. The mechanics deck and the electricity and magnetism deck drill the principles and definitions behind these problems, so that step 3 comes faster.

A weekly study routine for physics

Physics builds week on week. Rotation uses forces and energy; circuits use potential; magnetism uses vectors and circuits. Falling behind for two weeks costs more than it does in most courses, so a steady routine matters more than long sessions.

The end-of-week mixed set is the part students skip and the part that matters most. On a test, you are not told which chapter a problem comes from. Mixing old and new problems trains you to choose the principle, which is exactly the skill being graded. Dunlosky and colleagues (2013) rated practice testing and spreading study over time as the two most useful study techniques in their review; a mixed weekly set does both.

Before a midterm, switch to timed practice from past exams if your department posts them. Our final exam study plan lays out how to space that over two or three weeks. If calculus is the bottleneck, the first-year calculus guide covers the derivative and integral skills physics leans on.

Common mistakes in first-year physics

• Mixing units. Grams instead of kilograms, centimetres instead of metres, µC instead of C. Convert everything to SI in step 2.
• Missing a force. Normal force, tension and friction are easy to forget. Every contact with a surface or rope is a force on your diagram.
• Treating mass as a force. The weight is mg, in newtons. A "5 kg force" is not a thing in an SI answer.
• Sign errors with vectors. Pick a positive direction and keep it. A ball thrown up has a negative acceleration if up is positive.
• Using a formula outside its conditions. The constant-acceleration equations fail if acceleration changes; energy conservation fails if there is friction you have not accounted for.
• Calculator radians. If an angle in degrees gives a strange sine, check the calculator mode.
• Reading solutions instead of solving. Following a solution feels like understanding. Test it by closing the solution and starting from a blank page.

Keep a short error log: one line for each mistake you make on homework, with the fix. Before a test, read the log. Most students find the same three or four slips account for most lost marks.

Resources that help

Your textbook's worked examples are the best free resource you have; work them yourself before reading the solution. For a structured second pass through the material, the university mechanics course and the fields and thermal physics course walk through the main ideas in short lessons. For the jump from grade 12, see our high school to university guide. Office hours and the tutorial centre exist for exactly the question "I got stuck at step 3"; bring your attempt so the TA can see where it went wrong.