Every year one or two students finish the school course early and tell me physics has become easy. I set them a different problem and watch the confidence drain away in about six minutes. That moment is worth describing, because what happens next decides whether they keep going or quietly decide the subject got boring.
Here’s the school version. A 2 kg block slides down a 30° incline with friction coefficient 0.2. Find the acceleration. Along the slope: a = g(sin θ − μ cos θ) = 9.8(0.500 − 0.2 × 0.866) = 9.8 × 0.327 = 3.2 m/s². One free-body diagram, one equation, done. This is the problem the textbook gives you after teaching you the method.
Now the harder version. The incline is a wedge of mass 3 kg sitting on smooth ice, free to slide. Find the acceleration of both the block and the wedge. The block pushes the wedge sideways, the wedge runs away underneath it, the normal force isn’t mg cos θ anymore, and you have two bodies with one constraint: the block stays on the surface. You need conservation of momentum in the horizontal direction, a kinematic constraint, and a free-body diagram for each object, all at once. The solution is maybe twelve lines of algebra where the school version was two. Physics gets wider here, and the width is what trips people.
Here’s the shape of the solution, which I’ll leave you to fill in. Write conservation of momentum in the horizontal direction, because the ice is smooth and nothing pushes the system sideways. Write the constraint that the block never leaves the wedge face. Draw both free-body diagrams and solve the system together. Three ideas, one set of equations. That combination is the jump, and it’s the same jump in every harder problem you’ll meet.
What actually changes
School problems are built to use exactly the law you just learned. Olympiad problems pick the law for you. A national olympiad problem might ask about a chain sliding off a table (variable mass, use energy) or a charged ball on a rotating hoop (constraints plus circular motion), and the hard step is always the same: choosing the tool. Problem books are how you build that instinct. There are classic collections, the kind with 2000 problems sorted by topic, where a student is expected to spend 40 minutes on a single question before looking at anything. University courses raise the floor again: mechanics rebuilt on energy and later on Lagrangians, electromagnetism rebuilt on vector calculus. The equations from school survive as special cases.
The students who handle this well share a habit. They keep a notebook of their failed attempts, they reread problems they couldn’t do, and they treat a solution manual as a source of methods rather than answers. The ones who struggle treat difficulty as evidence of talent running out.
When I hand out a diagnostic set of ten olympiad problems, I watch a different number than the score. I measure how long the student works on the unsolved ones before giving up. Twenty minutes of honest attempts beats a fast surrender every time, and it’s the single best predictor I have of who survives the jump.
How I’d choose a paid course
At some point you’ll consider paying for help: an olympiad training program, a university-prep course, a tutor. Some are worth the money and some are expensive video folders. Since I can’t recommend specific products without knowing your situation, here’s the checklist I give parents, in order of weight.
First, find the problem sets before you pay. A serious course publishes its syllabus, and the syllabus lists problems. Topics are headings; problems are the product. “Ten hours of mechanics lectures” is a schedule; “40 graded problems with written feedback” is a course. Count the graded problems, because that’s what you’re buying. Second, ask who reads your solutions. A human commenting on your work is worth several times the same content without feedback. Third, look for sample lessons, and judge them the way you’d judge a teacher: does the person do calculations on screen, or narrate over slides? A sample lesson should show someone writing an equation, checking units, making a mistake, and catching it. Slide narrations sell comfort. Calculations sell physics. Fourth, check the refund policy and the class size. Fifth, ignore the certificates.
Pacing belongs in the price too. Self-paced courses finish fewer students than scheduled ones, because deadlines are part of the product. If a program has weekly problem sessions with dates attached, that structure is worth real money, and I’d pay for it before I’d pay for extra video hours.
Here’s the arithmetic I use on price. A course at $300 with 40 graded problem sets costs $7.50 per set with feedback. A $50 video series with no graded work costs $50 per set of nothing. The second one isn’t a bargain; it’s a different, lighter product, and it should be priced like one. When a program costs real money, ask directly: how many problems will someone grade for me? The answer tells you the value.
Tutoring follows the same logic in reverse. A tutor at $60 an hour who assigns you work between sessions and grades it is cheaper than a $30 an hour tutor who re-explains your homework to you. The work between the hours is where the learning happens.
Books and the long route
Before paying anyone, buy a used textbook. The standard first-year university texts cost $150 new and $25 used, and the older edition teaches the same physics. Add a problem book, a notebook dedicated to failed attempts, and a timer. Work a problem for 40 minutes before reading a solution; when you do read one, cover it line by line and ask where each step came from.
There’s a free route as well. University syllabi are public, libraries hold the textbooks, and problem sets circulate online. What you lose without a course is feedback and deadlines, so if you self-study, build both: a calendar with dates, and a partner who exchanges solutions with you and argues about the steps.
Olympiad camps and summer schools exist in most countries, and plenty of them have scholarships, so the price on the website is rarely the final price. Study groups help more than expected: explaining your solution out loud is where half the understanding gets built.
What I tell students running out of school physics: pick one course or one problem book, finish it, and keep the notebook. The problems make you good at physics. Now go back to the wedge and try the twelve lines yourself.