This comprehensive AP Physics 1 equation sheet contains all essential formulas you need for the AP Physics 1 exam. Our annotated formula reference includes detailed explanations, variable definitions, and pro tips for applying each equation effectively.
This physics equation sheet is perfect for exam prep, homework help, and quick reference during practice problems.
📖 Table of Contents
Unit 1: Kinematics
Velocity as a function of time
\[ v_{x} = v_{x0} + a_{x}t \]
Pro-Tip: Slope of v‑t graph = acceleration.
Position as a function of time
\[ x = x_{0} + v_{x0}t + \frac{1}{2}a_{x}t^{2} \]
Pro-Tip: At rest: \(v_{x0}=0\); constant velocity: \(a=0\).
Velocity–position (no time)
\[ v_{x}^{2} = v_{x0}^{2} + 2a_{x}(x – x_{0}) \]
Pro-Tip: Derived from work‑energy theorem.
Unit 2: Dynamics
Newton’s Second Law
\[ \sum \vec{F} = m\vec{a} \]
Pro-Tip: Always draw a free‑body diagram first.
Friction force
\[ |\vec{F}_f| \le \mu |\vec{F}_n| \]
Pro-Tip: Normal force is not always \(mg\).
Unit 3: Work, Energy & Power
Kinetic Energy
\[ K = \frac{1}{2}mv^{2} \]
Pro-Tip: Always positive (velocity squared).
Work by constant force
\[ W = F_{\parallel}d = Fd\cos\theta \]
Pro-Tip: Perpendicular forces do zero work.
Gravitational Potential Energy
\[ \Delta U_g = mg\Delta y \]
Pro-Tip: Only height difference matters.
Average Power
\[ P_{avg} = \frac{W}{\Delta t} \]
Pro-Tip: For constant velocity: \(P = Fv\).
Unit 4: Momentum & Impulse
Linear Momentum
\[ \vec{p} = m\vec{v} \]
Pro-Tip: Vector; direction matters for conservation.
Impulse-Momentum Theorem
\[ \Delta \vec{p} = \vec{F}_{avg}\Delta t \]
Pro-Tip: Longer impact time reduces average force (airbags).
Unit 5: Circular Motion & Rotation
Centripetal Acceleration
\[ a_c = \frac{v^2}{r} \]
Pro-Tip: Centripetal force is NET force toward center.
Torque
\[ \tau = r_{\perp}F = rF\sin\theta \]
Pro-Tip: Max torque when force ⟂ lever arm.
Newton’s 2nd Law (Rotation)
\[ \sum \tau = I\alpha \]
Pro-Tip: Rotational inertia depends on mass distribution.
Angular Momentum & Rotational KE
\[ L = I\omega,\quad K_{rot} = \frac{1}{2}I\omega^{2} \]
Pro-Tip: If net torque zero, \(L\) conserved (skater effect).
Unit 6: Simple Harmonic Motion
Hooke’s Law & Elastic PE
\[ F_s = -k\Delta x,\quad U_s = \tfrac{1}{2}k(\Delta x)^2 \]
Pro-Tip: Variable force → use energy conservation.
Period: mass-spring
\[ T_s = 2\pi\sqrt{\frac{m}{k}} \]
Pro-Tip: Independent of amplitude!
Period: simple pendulum
\[ T_p = 2\pi\sqrt{\frac{l}{g}} \]
Pro-Tip: Mass does not affect period.
Unit 7: Gravitation
Newton’s Law of Gravitation
\[ F_g = G\frac{m_1 m_2}{r^{2}} \]
Pro-Tip: Inverse‑square: double distance → force \(1/4\).
Gravitational Potential Energy
\[ U_G = -\frac{Gm_1 m_2}{r} \]
Pro-Tip: Negative potential energy well; zero at infinity.
Unit 8: Fluids
Density & Pressure
\[ \rho = \frac{m}{V},\quad P = \frac{F}{A} \]
Pro-Tip: Pascal’s principle: \(\frac{F_1}{A_1}=\frac{F_2}{A_2}\) for hydraulic systems.
Hydrostatic Pressure
\[ P = P_0 + \rho g h \]
Pro-Tip: Shape of container irrelevant – only depth matters.
Buoyant Force (Archimedes)
\[ F_b = \rho_{\text{fluid}} V_{\text{disp}} g \]
Pro-Tip: Use density of fluid, not object!
Continuity Equation
\[ A_1 v_1 = A_2 v_2 \]
Pro-Tip: Narrow pipe → faster flow (mass conservation).
Bernoulli’s Equation
\[ P_1 + \rho g y_1 + \frac12\rho v_1^2 = P_2 + \rho g y_2 + \frac12\rho v_2^2 \]
Pro-Tip: Derives Torricelli: \(v=\sqrt{2gh}\) if both ends open.
Complete AP Physics 1 Formula Sheet Guide
This comprehensive AP Physics 1 equation sheet contains all essential formulas you need for the exam. It covers:
- Kinematics equations and motion formulas
- Newton’s laws and dynamics equations
- Work, energy, and power formulas
- Momentum and impulse equations
- Rotational motion and torque formulas
- Simple harmonic motion equations
- Gravitation and fluid mechanics formulas
This formula sheet is ideal for exam preparation, homework help, and quick review.
What Makes This Equation Sheet Different?
Every key equation is paired with practical insights and AP exam strategies.
For example:
- Centripetal force is not a new force; it is the net force directed toward the center.
- The normal force is not always equal to mg.
- Perpendicular forces do zero work.
- A longer collision time reduces average impact force.
This approach helps you move from memorization to true understanding.
How to Use This AP Physics 1 Equation Sheet
You can:
- Download the PDF for offline study.
- Print it and annotate formulas.
- Keep it open while solving practice problems.
- Review it on your phone or tablet.
- Use it for last-minute revision before the exam.
Why AP Physics 1 Students Need a Formula Sheet
AP Physics 1 emphasizes conceptual understanding and algebra-based problem solving. Knowing the formulas is essential, but understanding when and why to apply them is even more important.
A well-organized equation sheet helps you:
- Save time during review.
- Connect related concepts.
- Identify commonly tested relationships.
- Avoid memorization mistakes.