15 Common Mistakes When Studying Physics (And How to Fix Them) | LearnByTeaching.ai
Physics requires translating real-world situations into mathematical models, and most mistakes happen at this translation step — not in the math itself. These 15 mistakes span mechanics, energy, and problem-solving habits, representing the traps that catch students from AP Physics through undergraduate courses.
Skipping the free-body diagram
Students jump straight to equations without drawing a free-body diagram (FBD), missing forces or getting directions wrong. The FBD is the single most important problem-solving tool in mechanics.
A student solving for tension in a rope holding a hanging mass forgets to include the gravitational force in their diagram, or draws tension pointing downward instead of along the rope away from the object.
How to fix it
Draw a free-body diagram for EVERY mechanics problem, even simple ones. Isolate the object, draw all contact forces and field forces (gravity), and label each with a variable. Then and only then write Newton's second law.
Memorizing formulas without understanding when to apply them
Students accumulate a sheet of equations and try to match problems to formulas by surface features rather than identifying the underlying physical principle.
A student uses v = v0 + at for a projectile at the top of its arc, not realizing this is a constant-acceleration formula for one dimension and must be applied separately to x and y components.
How to fix it
For every problem, first identify the principle (Newton's laws, energy conservation, momentum conservation), then select the relevant equations. Ask: what kind of problem is this, and what principle governs it?
Ignoring vector decomposition
Students treat forces, velocities, and accelerations as scalars or fail to decompose vectors into components along chosen axes. This is the most fundamental mathematical skill in physics.
A student solving for the acceleration of a block on an inclined plane uses mg for the force along the plane instead of mg sin(theta), because they didn't decompose the gravitational force into components parallel and perpendicular to the surface.
How to fix it
Always choose a coordinate system and decompose all vectors into components along those axes. For inclined planes, use axes parallel and perpendicular to the surface. Write separate equations for each component.
Confusing velocity, speed, acceleration, and force
Students conflate these distinct quantities, particularly believing that zero velocity means zero acceleration or that force is needed to maintain constant velocity.
A student says 'the ball at the top of its trajectory has zero acceleration because it momentarily stops' — confusing zero velocity with zero acceleration. Gravity acts throughout the trajectory.
How to fix it
Define each quantity precisely: velocity is rate of change of position, acceleration is rate of change of velocity, force causes acceleration. An object can have zero velocity and nonzero acceleration (ball at peak), or nonzero velocity and zero acceleration (constant speed).
Not checking units throughout calculations
Students compute numerical answers without tracking units, missing errors that would be obvious if units were carried through every step.
A student calculates kinetic energy as (1/2)(2 kg)(3 m/s) = 3, missing the squared velocity, but doesn't catch the error because they didn't track that the result should be in kg*m^2/s^2 (joules).
How to fix it
Write units on every number in every step. The final units must match what you expect (energy in joules, force in newtons, etc.). If they don't, you've made an error somewhere. Dimensional analysis catches most calculation mistakes.
Misapplying conservation of energy
Students use energy conservation without accounting for all forms of energy or work done by non-conservative forces like friction.
A student sets mgh = (1/2)mv^2 for a block sliding down a rough incline, forgetting that friction converts some potential energy into thermal energy, so the block arrives at the bottom slower than predicted.
How to fix it
Write the full energy conservation equation: KE_initial + PE_initial + W_non-conservative = KE_final + PE_final. Always ask: are there non-conservative forces (friction, air resistance, applied forces) doing work?
Confusing mass and weight
Students use mass and weight interchangeably, leading to errors in force calculations, especially in problems involving different gravitational environments.
A student says 'the weight of the object is 5 kg' — kg is a unit of mass, not weight. The weight is mg = 5 kg * 9.8 m/s^2 = 49 N.
How to fix it
Mass (kg) is the amount of matter; weight (N) is the gravitational force on that matter (W = mg). Always convert mass to weight using W = mg before using it in force equations.
Treating Newton's third law pairs as acting on the same object
Students identify action-reaction force pairs but incorrectly place both forces on the same object, causing them to cancel in their free-body diagram.
A student draws the normal force and gravitational force on a book on a table as a Newton's third law pair. They're not — the third law pair of the book's weight is the book pulling the Earth upward; the normal force pairs with the book pushing down on the table.
How to fix it
Newton's third law pairs always act on DIFFERENT objects. If object A pushes on object B, then B pushes back on A with equal and opposite force. Forces on the same object in a FBD are not third-law pairs.
Using the wrong sign convention for work and energy
Students are inconsistent with positive and negative signs for work, potential energy, and forces, leading to answers with the wrong sign or magnitude.
A student calculates work done by gravity on a falling object as negative (W = Fd cos 180°) because they used the displacement as upward, getting the wrong sign for kinetic energy gained.
How to fix it
Choose a consistent sign convention at the start: define positive direction, use it throughout. For work, W = F*d*cos(theta) where theta is the angle between force and displacement. Gravity does positive work when an object falls if downward is positive displacement.
Not drawing diagrams for non-mechanics problems
Students draw FBDs for mechanics but skip diagrams for circuits, optics, and wave problems, where visual representations are equally important.
A student tries to solve a circuit problem by writing equations directly without drawing the circuit diagram and labeling current directions, leading to sign errors in Kirchhoff's loop rule.
How to fix it
Draw a diagram for EVERY physics problem: circuit diagrams with labeled currents, ray diagrams for optics, wave diagrams for interference, PV diagrams for thermodynamics. The diagram is your roadmap.
Studying by reading solutions instead of solving problems
Students read worked examples and think they understand, but can't solve similar problems independently. Reading solutions creates an illusion of competence.
A student reads through 20 solved problems in the textbook and feels prepared, but can't solve the first homework problem because they never practiced the problem-solving process themselves.
How to fix it
Attempt every problem for at least 15 minutes before looking at solutions. Struggle is where learning happens. After checking the solution, close it and solve the problem again from scratch to verify you truly understand.
Rounding intermediate values too early
Students round numbers partway through multi-step calculations, accumulating rounding errors that produce a significantly wrong final answer.
A student rounds g from 9.8 to 10 m/s^2 early in a multi-step projectile problem, and the final answer is off by 15% — enough to get the problem marked wrong.
How to fix it
Keep at least 3-4 significant figures in all intermediate calculations and only round the final answer. Better yet, solve symbolically as long as possible and substitute numbers at the end.
Failing to sanity-check answers
Students compute an answer and move on without checking whether it makes physical sense — a car traveling at 10,000 m/s or a negative mass should trigger alarm bells.
A student calculates that a baseball thrown at 30 m/s reaches a height of 4,500 meters and doesn't question it, when a quick estimate (max height ~ v^2/2g ~ 900/20 ~ 45 m) shows the answer is off by a factor of 100.
How to fix it
After every calculation, ask: does this answer make physical sense? Check order of magnitude, sign, and units. Compare with known values (human walking speed ~1.5 m/s, free fall acceleration ~10 m/s^2).
Confusing centripetal and centrifugal force
Students treat centrifugal force as a real force acting outward on an object in circular motion, when the only real force is centripetal (directed inward toward the center).
A student draws a free-body diagram for a car rounding a curve with both a centripetal force (friction pointing inward) and a centrifugal force pointing outward, resulting in a net force of zero — which contradicts the fact that the car is accelerating.
How to fix it
In an inertial reference frame, there is no centrifugal force. The centripetal force is the net inward force that causes circular motion. Identify the real force providing it (friction, tension, gravity, normal force).
Not practicing with timed problem sets
Students practice physics problems without time pressure, then are shocked when they can't finish exams. Physics exams test both understanding and fluency.
A student can solve every homework problem given unlimited time but only finishes 60% of the exam because they spend too long on each problem without a strategy for time allocation.
How to fix it
Practice with timed problem sets before exams. Allocate time per problem proportional to its point value. If stuck for more than 2 minutes, write down what you know, set up what you can, and move on — partial credit matters.
Quick Self-Check
- Can you draw a correct free-body diagram for an object on an inclined plane with friction?
- Can you explain the difference between velocity and acceleration using a real-world example?
- Can you solve a conservation of energy problem that includes friction?
- Can you decompose a force vector into components along any pair of perpendicular axes?
- Can you identify which Newton's law applies to a given scenario and set up the equation?
Pro Tips
- ✓Solve every problem symbolically first (using variables), then plug in numbers at the end — this makes it easier to check units and identify errors.
- ✓For every problem: draw a diagram, list knowns and unknowns, identify the principle, set up equations, solve, then check units and reasonableness.
- ✓Use PhET simulations (phet.colorado.edu) to build physical intuition before doing math — seeing forces and motion animated helps tremendously.
- ✓Study in pairs and explain your solution approach out loud — if you can't explain why you chose energy conservation over Newton's second law, you don't fully understand the problem.
- ✓Keep a personal 'mistake log' of errors you've made on homework and exams — reviewing it before tests is more valuable than re-reading notes.