AP Physics Formulas Cheat Sheet with Explanation

Physics can sometimes feel overwhelming, but having a well-organized cheat sheet can make a huge difference. Below, you'll find a collection of essential formulas grouped by topic to help you tackle AP Physics problems. Short explanations are included to guide you in how to use each formula.

Need help mastering AP Physics? Sign up for group tutoring with Physics Luminary LLC. Call 804-566-9251 or email hello@physicsluminary.com for more information!

Kinematics Equations

$$ v_x = v_{x0} + a_x t $$

Use this to find final velocity when you know initial velocity, acceleration, and time.

$$ x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2 $$

This equation helps find displacement, given initial velocity, acceleration, and time.

$$ v_x^2 = v_{x0}^2 + 2 a_x (x - x_0) $$

Use this when you need to find velocity without knowing time but knowing displacement and acceleration.

Center of Mass

$$ \vec{x}_{\mathrm{cm}} = \frac{\sum m_i \vec{x}_i}{\sum m_i} $$

Calculates the center of mass of a system with multiple masses.

Newton's Second Law

$$ \vec{a}_{\mathrm{sys}} = \frac{\sum \vec{F}_{\mathrm{sys}}}{m_{\mathrm{sys}}} = \frac{\vec{F}_{\mathrm{net}}}{m_{\mathrm{sys}}} $$

Relates the net force on a system to its acceleration.

Gravitational Force

$$ |\vec{F}_g| = G \frac{m_1 m_2}{r^2} $$

Newton's law of universal gravitation. Use this to find the gravitational force between two masses.

Friction Force

$$ |\vec{F}_f| \leq |\mu \vec{F}_n| $$

This gives the maximum static or kinetic friction force. Useful for solving friction problems.

Spring Force

$$ \vec{F}_s = -k \Delta \vec{x} $$

Use this to find the restoring force in a spring (Hooke's Law).

Centripetal Acceleration

$$ a_c = \frac{v^2}{r} $$

This calculates the centripetal acceleration needed to keep an object moving in a circle.

Kinetic Energy

$$ K = \frac{1}{2} m v^2 $$

The kinetic energy of an object based on its mass and velocity.

Work

$$ W = F_{\|} d = F d \cos (\theta) $$

Work done by a force applied over a distance. Use this for forces at angles to motion.

Work-Energy Theorem

$$ \Delta K = \sum W_i = \sum F_{\|,i} d_i $$

This relates the change in kinetic energy to the net work done on an object.

Spring Potential Energy

$$ \Delta U_s = \frac{1}{2} k (\Delta x)^2 $$

The potential energy stored in a compressed or stretched spring.

Gravitational Potential Energy

$$ U_G = - \frac{G m_1 m_2}{r} $$

Gravitational potential energy between two masses.

$$ \Delta U_g = m g \Delta y $$

Gravitational potential energy relative to the Earth's surface.

Power

$$ P_{\text{avg}} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t} $$

Average power, or the rate at which work is done or energy is transferred.

$$ P_{\text{inst}} = F_{\|} v = F v \cos(\theta) $$

Instantaneous power, useful when force and velocity are known.

Momentum and Impulse

$$ \vec{p} = m \vec{v} $$

Momentum of an object, mass times velocity.

$$ \vec{F}_{\text{net}} = \frac{\Delta \vec{p}}{\Delta t} = m \frac{\Delta \vec{v}}{\Delta t} = m \vec{a} $$

Newton's second law in terms of momentum.

$$ \vec{J} = \vec{F}_{\text{avg}} \Delta t = \Delta \vec{p} $$

Impulse, or the change in momentum caused by a force over time.

$$ \vec{v}_{\text{cm}} = \frac{\sum \vec{p}_i}{\sum m_i} = \frac{\sum m_i \vec{v}_i}{\sum m_i} $$

Velocity of the center of mass of a system of particles.

Rotational Kinematics

$$ \omega = \omega_0 + \alpha t $$

Angular velocity after a time, given initial angular velocity and angular acceleration.

$$ \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 $$

Angular displacement given angular acceleration, time, and initial angular velocity.

$$ \omega^2 = \omega_0^2 + 2 \alpha (\theta - \theta_0) $$

Final angular velocity after an angular displacement, without using time.

$$ v = r \omega $$

Linear velocity from angular velocity in a rotating system.

$$ a_T = r \alpha $$

Tangential acceleration from angular acceleration.

Torque

$$ \tau = r_{\perp} F = r F \sin (\theta) $$

Torque, or the rotational force applied at a radius.

Moment of Inertia

$$ I = \sum m_i r_i^2 $$

Moment of inertia for point masses in a system.

$$ I' = I_{\text{cm}} + M d^2 $$

Parallel axis theorem, relating moment of inertia about a center of mass to another axis.

Rotational Acceleration (System-Wide)

$$ \alpha_{\text{sys}} = \frac{\Sigma \tau}{I_{\text{sys}}} = \frac{\tau_{\text{net}}}{I_{\text{sys}}} $$

System-wide rotational acceleration, from net torque and moment of inertia.

Rotational Power and Work

$$ K = \frac{1}{2} I \omega^2 $$

Kinetic energy of a rotating object.

$$ W = \tau \Delta \theta $$

Work done in rotational motion, using torque and angular displacement.

Angular Momentum

$$ L = I \omega $$

Angular momentum from moment of inertia and angular velocity.

$$ L = r m v \sin \theta $$

Angular momentum of a point mass moving in a straight line.

$$ \Delta L = \tau \Delta t $$

Change in angular momentum due to torque over time (impulse).

$$ \Delta x_{\text{cm}} = r \Delta \theta $$

Linear displacement of the center of mass in rotational motion.

Oscillations

$$ T = \frac{1}{f} $$

Period of oscillation, inverse of frequency.

$$ T_s = 2 \pi \sqrt{\frac{m}{k}} $$

Period of a mass-spring system.

$$ T_p = 2 \pi \sqrt{\frac{\ell}{g}} $$

Period of a simple pendulum.

$$ x = A \cos (2 \pi f t) $$

Position of an oscillating object at time t, using cosine.

$$ x = A \sin (2 \pi f t) $$

Position of an oscillating object at time t, using sine.

Fluid Mechanics

$$ \rho = \frac{m}{V} $$

Density, mass per unit volume.

$$ P = \frac{F_{\perp}}{A} $$

Pressure, force applied perpendicularly per unit area.

$$ P = P_0 + \rho g h $$

Absolute pressure at a depth in a fluid.

$$ P_{\text{gauge}} = \rho g h $$

Gauge pressure, pressure above atmospheric pressure.

$$ F_b = \rho V g $$

Buoyant force on an object submerged in a fluid.

Continuity Equation

$$ A_1 v_1 = A_2 v_2 $$

Flow rate of an incompressible fluid through two sections of a pipe.

Bernoulli's Equation

$$ P_1 + \rho g y_1 + \frac{1}{2} \rho v_1^2 = P_2 + \rho g y_2 + \frac{1}{2} \rho v_2^2 $$

Bernoulli's equation, relating pressure, velocity, and height in a moving fluid.

Comments

Post a Comment

Popular posts from this blog

Solving Elevator Problems in Physics

Elevator problems are a great way to understand the concept of apparent weight and how forces interact in an accelerating system. In this post, we’ll break down elevator scenarios step by step and show you how to solve for apparent weight changes during upward and downward acceleration. Table of Contents Step-by-Step Recipe for Solving Elevator Problems Worked Example: Apparent Weight in an Elevator Key Takeaways Step-by-Step Recipe for Solving Elevator Problems 1. Identify all the forces acting on the person or object in the elevator. The forces involved are: Gravitational force \( F_g = m \cdot g \) (downward, always the same). Normal force \( F_n \) (the force exerted by the scale or floor, this is the apparent weight). 2. Set up the problem based on the acceleration of the elevator. If the elevator is accelerating upwards or downwards, it changes the apparent weight felt by the person or object. ...
Read more

AP Physics Formula Cheat Sheet

Physics can sometimes feel overwhelming, but having a well-organized cheat sheet can make a huge difference. Below, you'll find a collection of essential formulas grouped by topic to help you tackle AP Physics problems. Kinematics Equations $$ v_x = v_{x0} + a_x t $$ $$ x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2 $$ $$ v_x^2 = v_{x0}^2 + 2 a_x (x - x_0) $$ Center of Mass $$ \vec{x}_{\mathrm{cm}} = \frac{\sum m_i \vec{x}_i}{\sum m_i} $$ Newton's Second Law $$ \vec{a}_{\mathrm{sys}} = \frac{\sum \vec{F}_{\mathrm{sys}}}{m_{\mathrm{sys}}} = \frac{\vec{F}_{\mathrm{net}}}{m_{\mathrm{sys}}} $$ Gravitational Force $$ |\vec{F}_g| = G \frac{m_1 m_2}{r^2} $$ Friction Force $$ |\vec{F}_f| \leq |\mu \vec{F}_n| $$ Spring Force $$ \vec{F}_s = -k \Delta \vec{x} $$ Centripetal Acceleration $$ a_c = \frac{v^2}{r} $$ Kinetic Energy $$ K = \frac{1}{2} m v^2 $$ Work $$ W = F_{\|} d = F d \cos (\theta) $$ Work-...
Read more

Why Maximum Range Occurs at 45 Degrees?

Have you ever wondered why a projectile travels the farthest when launched at a 45-degree angle ? Whether you're a student tackling kinematics problems or just someone intrigued by the physics of motion, this blog post is for you. We'll delve into the fundamentals of projectile motion, derive the equations that explain maximum range, and understand why that magical 45-degree angle is the key to achieving it. Table of Contents Introduction to Projectile Motion Understanding the Components of Motion Deriving the Range Equation Maximizing the Range: Why 45 Degrees? Practical Considerations Common Misconceptions Conclusion Introduction to Projectile Motion Projectile motion is a form of motion where an object moves in a bilaterally symmetrical, parabolic path under the action of gravity alone. Classic examples include a football being kicked, a cannonball fired from a cannon, or water sprayed from a hose. Und...
Read more