AP Physics 1 Equation Sheet: How to Use It on the Exam

The AP Physics 1 equation sheet is a reference the College Board gives you in the exam, so you do not have to memorise every formula. The marks, though, come from picking the right equation, rearranging it and checking the answer. This guide explains how to use the equation sheet on the exam: what it gives you, what you must know without it, and how to use it with a worked example for each unit.

What the equation sheet gives you

Students often call it the AP Physics 1 formula sheet. It lists the key equations for each unit, with the symbols defined and the standard constants, such as g = 9.8 m/s². The full list, grouped by unit, is on our AP Physics 1 equation sheet page, and every equation can be tried in the Physics Formulas calculator.

The sheet does not explain the physics. It names the relationships but not what they mean, when they apply, or which one a question needs. Check the College Board's AP Physics 1 course page for the current version before your exam, because the sheet is revised from time to time.

What is not on the sheet (memorise these)

• Definitions. Work, power, impulse and torque are defined in words in the course, but the sheet only gives the equation. Know what each quantity means.
• Newton's laws and conservation laws in words. For example, momentum is conserved when the net external force on a system is zero, and energy is conserved when only conservative forces do work.
• Unit definitions. 1 N = 1 kg·m/s², 1 J = 1 N·m and 1 W = 1 J/s. Unit checks catch most algebra mistakes.
• Trigonometry. Resolving a force into components needs sin and cos of standard angles (sin 30° = 0.5, cos 60° = 0.5, sin 90° = 1).
• Sign conventions. Which direction is positive, and whether work or a torque is positive or negative, depend on the question.
• Which equation to choose. Matching the known quantities to the right relationship is the skill being tested.

AP Physics 1 Equations: Worked Examples, Unit by Unit

Kinematics

A car speeds up from 4 m/s to 20 m/s in 8 s. The acceleration is a = (v − v₀)/t = (20 − 4)/8 = 2.0 m/s². The distance is then (v₀ + v)t/2 = (4 + 20)/2 × 8 = 96 m, which comes from the average-velocity form, so you don't need the position equation.

Forces and circular motion

A 1200 kg car has a net force of 3000 N, so a = ΣF/m = 3000/1200 = 2.5 m/s². A 5.0 kg block on a flat table with μ = 0.30 has a maximum friction force of 0.30 × 5.0 × 9.8 = 14.7 N. A car taking a 50 m bend at 10 m/s has a_c = v²/r = 10²/50 = 2.0 m/s² towards the centre.

Energy and power

A 2.0 kg ball falls 5.0 m. It loses ΔU_g = mgΔy = 2.0 × 9.8 × 5.0 = 98 J of gravitational potential energy, which becomes kinetic energy. Its speed is then √(2K/m) = √(2 × 98 / 2) ≈ 9.9 m/s. If the 98 J is transferred in 2.0 s, the power is P = ΔE/Δt = 49 W.

Linear momentum

A 0.15 kg ball travelling at +20 m/s is hit back at −30 m/s. The change in momentum is Δp = m(v − v₀) = 0.15 × (−30 − 20) = −7.5 kg·m/s, so the impulse has magnitude 7.5 N·s. If the bat is in contact for 0.003 s, the average force is F = J/Δt = 7.5 / 0.003 = 2500 N.

Oscillations

A 0.50 kg mass on a spring with k = 200 N/m has T = 2π√(m/k) = 2π√(0.50/200) = 2π × 0.050 ≈ 0.31 s. A simple pendulum 1.0 m long has T = 2π√(ℓ/g) = 2π√(1.0/9.8) ≈ 2.0 s. Notice that the spring period does not depend on g, and the pendulum period does not depend on its mass.

Torque and rotation

A wrench 0.30 m long is pulled with 40 N at right angles to the handle. The torque is τ = rF sin θ = 0.30 × 40 × sin 90° = 12 N·m. If the bolt's rotational inertia is I = 0.60 kg·m², then α = τ/I = 12 / 0.60 = 20 rad/s².

Fluids

A 0.020 m³ object fully submerged in water feels a buoyant force of F_b = ρVg = 1000 × 0.020 × 9.8 ≈ 196 N. The pressure 10 m below a water surface is P = P₀ + ρgh ≈ 1.01 × 10⁵ + 1000 × 9.8 × 10 ≈ 2.0 × 10⁵ Pa. In a pipe where the area halves, continuity (A₁v₁ = A₂v₂) says the speed doubles.

A method that works on every question

1. Write down the knowns and the unknown, with units.
2. Find the unit the question is about and pick the equation that links exactly those quantities.
3. Rearrange with symbols first, then substitute numbers.
4. Check the units and whether the size of the answer is sensible.

The impulse and work-energy questions are where students most often lose marks, because the sheet offers two routes to the same answer. Choose the one with fewer unknowns.

Common mistakes

• Using a quantity without its sign. A decelerating car has negative acceleration; a force opposing motion does negative work.
• Mixing kinematic and energy equations. The kinematic form needs time or displacement; if neither is given, energy is usually quicker.
• Forgetting the angle. Torque and work both use sin θ or cos θ, so check whether the force is perpendicular to the lever arm or the displacement.
• Using degrees in a formula that needs radians. Angular velocity and angular acceleration are in rad/s and rad/s².

Frequently asked questions

Do you get an equation sheet on the AP Physics 1 exam?

Yes. The College Board provides an equation sheet with the equations and constants you need, and it is available in the exam. It lists the relationships but does not tell you which one to use or what the symbols mean in a particular problem, so practise choosing equations as well as reading them.

Is the AP Physics 1 equation sheet enough to pass?

No. The sheet gives the equations, but the marks come from explaining the physics, choosing the right relationship, showing your working and checking units. Students who only read the sheet usually struggle with multi-step questions.

What is not on the AP Physics 1 equation sheet?

The sheet does not define the quantities, state the conservation laws in words, or give unit definitions and trigonometric values. It also does not tell you the sign of an answer or which equation a question needs. Memorise these, and use the sheet for the formulas themselves.

How should I practise with the equation sheet?

Solve past questions with the sheet in front of you, then write one line for each equation saying what situation it is for. This matches the exam, where you have to choose the equation yourself.

Try it yourself

Open the Physics Formulas page and work the car example above by hand, then change the final speed to 30 m/s and find the new acceleration. For the rotation example, open the torque and rotation tool and check that your value of τ = rF sin θ matches what the tool shows when you use the same lever arm and angle.