AP Physics 1: Algebra-Based — Cheatsheet

Formulas & relationships

On the exam

• On the AP exam, always state your positive direction before plugging in numbers. Half of kinematics is bookkeeping — a consistent sign convention earns points that raw algebra cannot.
• When a problem gives you velocities and a distance but never mentions time, reach straight for v² = v₀² + 2aΔx. Recognizing that missing variable saves you from solving a needless quadratic.
• Free-response graph questions love the chain "slope of x–t → v, slope of v–t → a, area under v–t → Δx". Memorize those three links and you can convert between any pair of graphs.
• The classic AP trap: applying gravity to the horizontal axis. Horizontal velocity is constant for every projectile. Gravity changes only the vertical velocity. Keep the two axes in separate columns on your paper.
• On the AP exam, "equilibrium" does not mean "at rest." An object moving at constant velocity has zero acceleration, so its net force is also zero. Constant velocity and rest are the *same* dynamical situation.
• Draw the free-body diagram before writing a single equation. On free response, a correct FBD with properly labeled forces earns points even if your algebra later slips — and it prevents you from inventing forces that are not there.
• Watch the difference between "is it moving yet?" and "how fast does it slow down?" Use **static** friction (an inequality, up to μ_s N) to test whether motion starts; use **kinetic** friction (a fixed μ_k N) once it is already sliding.
• When a circular-motion problem asks for a force, first ask "which real force points toward the center?" Then set that force equal to mv²/r. Naming the actual force (tension, friction, gravity, normal) is what earns the reasoning point.
• Before computing work, check the angle between the force and the displacement. Perpendicular forces (normal force on a flat surface, gravity in horizontal motion, tension in circular motion) do exactly zero work — a favorite AP trap.
• You may place the h = 0 reference wherever it is most convenient — the floor, the tabletop, the ground below a cliff. Only the *change* in height between start and finish affects the physics, so choose the level that makes the arithmetic simplest.
• If a problem mentions friction or air resistance, mechanical energy is *not* conserved — the "missing" energy became heat. Write KE_i + PE_i = KE_f + PE_f + E_thermal and treat the thermal term as the energy removed.
• Remember that power and energy are different quantities: energy (joules) is the total transferred, power (watts) is the rate. A question asking "how quickly" or "per second" is about power; "how much total" is about energy or work.
• When asked why a safety feature reduces force, argue from J = FΔt with Δp fixed. The impulse (momentum change) is set by the collision, so a longer Δt forces a smaller F. Name the theorem to earn the reasoning point.
• For any "at rest, then flies apart" problem, set total momentum equal to zero. The pieces carry equal and opposite momenta, so the mass ratio is the inverse of the speed ratio — heavier means slower.
• Two equations, two situations: momentum conservation works for *every* collision, but the kinetic-energy conservation equation is only valid for collisions the problem calls elastic. Never assume energy is conserved unless told so.
• Internal forces never move the center of mass. Whenever a problem shows an object breaking apart or flexing with no external force, the CM keeps whatever motion it had — a fast way to reason about explosions and recoil.
• Watch the difference between angular speed ω (shared by the whole object) and linear speed v (larger the farther you are from the axis). A question about "a point on the rim" almost always wants v = rω, not ω.
• When a force is not perpendicular, do not forget the sinθ. A common error is using τ = rF and ignoring the angle; only the perpendicular component turns the object.
• On the AP formula sheet you are given I for standard shapes (hoop MR², solid disk ½MR², sphere ⅖MR²). You are not expected to derive them — just choose the right one and remember the pattern: mass farther out gives a bigger coefficient.
• Free-response equilibrium problems almost always need both conditions. Write ΣF = 0 and Στ = 0 as two separate equations — many setups are unsolvable from the force equation alone.
• In a "race down the ramp" question, the object that puts *less* energy into rotation (smaller I relative to mR²) ends up moving faster. That is a direct consequence of splitting mgh between ½mv² and ½Iω².
• Angular momentum is a vector along the rotation axis. On the AP exam its direction matters most in conservation problems, where the total vector — magnitude and direction — must stay constant.
• Conservation of angular momentum needs zero *external* torque. Internal changes — pulling in arms, dropping on clay — do not violate it. Check that nothing outside the system is applying a torque before you set L constant.
• For ramp-race questions, rank shapes by how much of mgh goes into rotation: sphere (⅖MR²) beats disk (½MR²) beats hoop (MR²). Mass and radius cancel out, so the *shape* alone decides the winner.
• A frequent SHM question asks "where is acceleration maximum / speed maximum?" Remember they are opposite: acceleration peaks at the extremes (max force), speed peaks at equilibrium (max KE).
• To change a pendulum’s period you must change its length or move it to a different g. Adding mass or (for small swings) changing the amplitude does nothing — a common distractor on the exam.
• Keep the units straight: period is seconds *per* cycle, frequency is cycles *per* second. When a problem gives "cycles in a time," divide cycles by time for frequency, then invert for period.
• The total energy of an oscillator scales with the *square* of the amplitude (E = ½kA²). Double the amplitude and you quadruple the energy — and the maximum speed only doubles, since v_max scales linearly with A.
• Distinguish gauge pressure (ρgh, the pressure from the fluid alone) from absolute pressure (P₀ + ρgh, which adds the atmosphere on top). Read the question carefully to see which is asked.
• For a floating object, the buoyant force exactly equals its weight (it is in equilibrium). The fraction submerged equals the ratio of the object’s density to the fluid’s density — a handy shortcut for iceberg-style problems.
• Continuity assumes an incompressible fluid and steady flow. On the AP exam it is almost always paired with Bernoulli’s equation: first use continuity to get the speeds, then feed them into Bernoulli for the pressures.
• Solve fluid-flow free-response in two steps: continuity (A₁v₁ = A₂v₂) gives the speeds, then Bernoulli (P + ½ρv² + ρgh = constant) gives the pressures. For horizontal pipes, drop the ρgh terms to simplify.
• If a free-response part says "the students plot the data so that the graph is linear", it is asking you to rearrange the equation into y = mx + b and name the axes. State what goes on each axis *and* what the slope represents — both are separate rubric points.
• Write "up is positive" at the top of any projectile free-response and use it consistently. Rubrics award the sign convention, and a single flipped sign in the vertical equation usually propagates into every later part of the question.
• Draw a separate free-body diagram for each object, even when you plan to use the system shortcut. Rubrics award the diagrams independently of the algebra, and a labeled diagram with no numbers still earns points.
• On any circular-motion free-response, write "toward the center is positive" and then sum only the real forces. If your equation contains a term called F_c alongside tension and weight, you have counted the same force twice.
• On a free-response, state your system and your zero of potential energy in words before writing any equation. Both are rubric points on energy questions, and choosing the ground as U = 0 makes almost every problem arithmetically cleaner.
• When a graph question gives a force in newtons and a position axis in centimeters, convert before computing the area. Unit slips on graph-area questions are more common than conceptual errors, and the rubric does not distinguish between the two.
• Draw and label a before/after sketch with your axes marked before writing anything. On two-dimensional momentum free-responses, the two component equations are separate rubric points, and setting them up correctly earns credit even if the arithmetic goes wrong.
• When a free-response has a collision followed by a swing, slide or rise, it almost always wants momentum for the collision and energy for what follows. Using energy through the collision itself is the single most common way students lose the whole question.
• The AP equation sheet gives you the rotational inertia coefficients, so do not memorize them — but do learn their *order* (sphere < disk < hoop). Ranking questions ask which object wins a race or needs more torque, and the ranking alone answers them.
• State your pivot explicitly and label the sign convention (counterclockwise positive is standard). Rubrics award the correct torque equation, and an equation with an unstated pivot cannot be graded even when the numbers are right.
• Whenever a problem says "rolls without slipping", write v = ωR and a = αR immediately. That constraint is the equation that closes the system, and rubrics award it as a separate point from the dynamics equations it connects.
• A "which arrives first" ranking task is answered entirely by the rotational inertia coefficient. Say that the object with the smaller coefficient devotes a smaller fraction of its energy to rotation and therefore has more translational speed — that reasoning is the rubric point, not the number.
• Say "no net external torque acts about the axis, so angular momentum is conserved" in words before writing I₁ω₁ = I₂ω₂. Naming the condition is a rubric point independent of the algebra, and it forces you to check whether the condition actually holds.
• For a collision that then leads to a swing, write two clearly separated stages on your paper: "Stage 1, collision — angular momentum" and "Stage 2, swing — energy". Rubrics score the two stages independently, so a correct stage 2 still earns points even after a slip in stage 1.
• Graph questions often supply one curve and ask you to sketch another. Mark the moments where the given curve is zero and where it peaks, then use the rule that peaks in one graph line up with zeros in the next. Sketching from those anchor points is far more reliable than trying to draw a sinusoid freehand.
• Experimental-design questions want a *procedure*, not just an equation: name the quantity you vary, the quantities you hold constant, the instrument you use, and what you plot. Each of those is typically its own rubric point, and they can be earned even if the final calculation goes wrong.
• On buoyancy free-responses, start by drawing a free-body diagram with weight down and buoyant force up, plus tension or a normal force if present. Every buoyancy question in this unit is a force balance, and the diagram earns its own rubric point.
• Check that every term in a Bernoulli equation comes out in pascals before you solve. P, ½ρv² and ρgh must all have the same units, and a term that does not is the fastest way to catch a substitution error under time pressure.

How to get a 5

• Always draw a labeled free-body diagram before equations — it's often worth points and prevents sign errors.
• For the paragraph response, write complete sentences with physics vocabulary and cite the principle (e.g., "by conservation of momentum") — bullet fragments lose credit.
• Start from a fundamental principle and derive symbolically before plugging in numbers; the exam rewards the correct relationship even if arithmetic fails.
• When justifying, connect to a conservation law or Newton's laws explicitly and address the specific scenario — explain WHY, don't restate the answer.
• Draw the free-body diagram before writing any equation and label each force by its physical agent (Earth, surface, string). Invented forces such as “centrifugal force” or “force of motion” lose points immediately on the AP scoring guidelines.
• On “justify your answer” and paragraph-length response parts, name a specific principle (Newton’s third law, conservation of angular momentum, the work–energy theorem) and tie it to the given numbers or graph. Restating the answer in different words earns nothing.
• Solve symbolically first, then substitute. A symbolic result such as h = Us/(mg) instantly answers the “what if the mass doubles?” follow-up and earns partial credit even if the arithmetic later slips.
• For experimental design questions, name the equipment, state what you measure and how many trials, and say how you would linearize the data (plot T² against m, not T against m). Then explain what the slope means physically.
• Expect proportional reasoning on the multiple-choice section: fields obey inverse squares (double r → quarter g), kinetic and spring energies go as the square (double v → quadruple K), and pipe speeds scale with area rather than radius.

Key terms