Velocity

\[ v = \frac{\Delta x}{\Delta t} \]

Where: \(v\) = velocity (m/s), \(\Delta x\) = displacement (m), \(\Delta t\) = time interval (s)

Application: Calculates average velocity as the rate of change of position over time

Acceleration

\[ a = \frac{\Delta v}{\Delta t} \]

Where: \(a\) = acceleration (m/s²), \(\Delta v\) = change in velocity (m/s), \(\Delta t\) = time interval (s)

Application: Measures the rate of change of velocity over time

Equations of Motion (Constant Acceleration)

\[ v = v_0 + at \]

\[ x = x_0 + v_0t + \frac{1}{2}at^2 \]

\[ v^2 = v_0^2 + 2a(x - x_0) \]

Where: \(v_0\) = initial velocity, \(v\) = final velocity, \(a\) = acceleration, \(t\) = time, \(x\) = position

Application: The SUVAT equations describe motion with constant acceleration

Newton's Second Law

\[ F = ma \]

Where: \(F\) = force (N), \(m\) = mass (kg), \(a\) = acceleration (m/s²)

Application: Force equals mass times acceleration - the fundamental equation of dynamics

Weight

\[ W = mg \]

Where: \(W\) = weight (N), \(m\) = mass (kg), \(g\) = gravitational acceleration (≈9.81 m/s²)

Application: Calculates the gravitational force on an object

Momentum

\[ p = mv \]

Where: \(p\) = momentum (kg·m/s), \(m\) = mass (kg), \(v\) = velocity (m/s)

Application: Momentum is conserved in closed systems - key for collision problems

Work

\[ W = Fd\cos\theta \]

Where: \(W\) = work (J), \(F\) = force (N), \(d\) = displacement (m), \(\theta\) = angle between force and displacement

Application: Work is energy transferred by a force acting through a distance

Kinetic Energy

\[ KE = \frac{1}{2}mv^2 \]

Where: \(KE\) = kinetic energy (J), \(m\) = mass (kg), \(v\) = velocity (m/s)

Application: Energy of motion - depends on mass and velocity squared

Gravitational Potential Energy

\[ PE = mgh \]

Where: \(PE\) = potential energy (J), \(m\) = mass (kg), \(g\) = gravitational acceleration (m/s²), \(h\) = height (m)

Application: Energy stored due to position in a gravitational field

Power

\[ P = \frac{W}{t} = Fv \]

Where: \(P\) = power (W), \(W\) = work (J), \(t\) = time (s), \(F\) = force (N), \(v\) = velocity (m/s)

Application: Rate of doing work or transferring energy

Ohm's Law

\[ V = IR \]

Where: \(V\) = voltage (V), \(I\) = current (A), \(R\) = resistance (Ω)

Application: Fundamental relationship between voltage, current, and resistance

Electric Power

\[ P = IV = I^2R = \frac{V^2}{R} \]

Where: \(P\) = power (W), \(I\) = current (A), \(V\) = voltage (V), \(R\) = resistance (Ω)

Application: Rate of electrical energy transfer - multiple equivalent forms

Resistors in Series

\[ R_{total} = R_1 + R_2 + R_3 + ... \]

Application: Total resistance increases when resistors are connected end-to-end

Resistors in Parallel

\[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... \]

Application: Total resistance decreases when resistors are connected side-by-side

Coulomb's Law

\[ F = k\frac{q_1q_2}{r^2} \]

Where: \(F\) = force (N), \(k\) = Coulomb's constant (8.99×10⁹ N·m²/C²), \(q_1, q_2\) = charges (C), \(r\) = distance (m)

Application: Force between two point charges - inverse square law

Magnetic Force on Moving Charge

\[ F = qvB\sin\theta \]

Where: \(F\) = force (N), \(q\) = charge (C), \(v\) = velocity (m/s), \(B\) = magnetic field (T), \(\theta\) = angle

Application: Force on a charged particle moving in a magnetic field

Wave Speed

\[ v = f\lambda \]

Where: \(v\) = wave speed (m/s), \(f\) = frequency (Hz), \(\lambda\) = wavelength (m)

Application: Universal wave equation - applies to all waves

Period and Frequency

\[ T = \frac{1}{f} \]

Where: \(T\) = period (s), \(f\) = frequency (Hz)

Application: Period is the time for one complete oscillation; frequency is oscillations per second

Snell's Law (Refraction)

\[ n_1\sin\theta_1 = n_2\sin\theta_2 \]

Where: \(n_1, n_2\) = refractive indices, \(\theta_1, \theta_2\) = angles of incidence and refraction

Application: Describes how light bends when passing between different media

Lens Equation

\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]

Where: \(f\) = focal length, \(d_o\) = object distance, \(d_i\) = image distance

Application: Relates object, image, and focal distances for lenses and mirrors

Heat Energy

\[ Q = mc\Delta T \]

Where: \(Q\) = heat energy (J), \(m\) = mass (kg), \(c\) = specific heat capacity (J/kg·K), \(\Delta T\) = temperature change (K or °C)

Application: Energy required to change the temperature of a substance

Ideal Gas Law

\[ PV = nRT \]

Where: \(P\) = pressure (Pa), \(V\) = volume (m³), \(n\) = number of moles, \(R\) = gas constant (8.314 J/mol·K), \(T\) = temperature (K)

Application: Relates pressure, volume, and temperature for ideal gases

First Law of Thermodynamics

\[ \Delta U = Q - W \]

Where: \(\Delta U\) = change in internal energy (J), \(Q\) = heat added (J), \(W\) = work done by system (J)

Application: Energy conservation - change in internal energy equals heat added minus work done

Einstein's Mass-Energy Equivalence

\[ E = mc^2 \]

Where: \(E\) = energy (J), \(m\) = mass (kg), \(c\) = speed of light (3×10⁸ m/s)

Application: Mass and energy are interchangeable - basis of nuclear energy

Photon Energy

\[ E = hf = \frac{hc}{\lambda} \]

Where: \(E\) = photon energy (J), \(h\) = Planck's constant (6.626×10⁻³⁴ J·s), \(f\) = frequency (Hz), \(\lambda\) = wavelength (m)

Application: Energy of electromagnetic radiation - quantum nature of light

De Broglie Wavelength

\[ \lambda = \frac{h}{p} = \frac{h}{mv} \]

Where: \(\lambda\) = wavelength (m), \(h\) = Planck's constant, \(p\) = momentum (kg·m/s), \(m\) = mass (kg), \(v\) = velocity (m/s)

Application: Wave-particle duality - all matter has wave properties

📚 Understand, Don't Memorize

Focus on understanding the physical meaning behind each equation. Know what each variable represents and how they relate to each other conceptually.

🔢 Check Units

Always verify that your units are consistent. Unit analysis can help catch mistakes and ensure you're using the right equation.

✏️ Practice Problems

Work through many practice problems to develop intuition for when and how to apply each equation in different contexts.

🎯 Identify the Right Equation

Learn to recognize what type of problem you're solving and which equations are relevant. Draw diagrams to visualize the situation.

🔗 See Connections

Many equations are related. For example, \(F=ma\) connects to \(W=Fd\) which connects to \(KE=\frac{1}{2}mv^2\). Understanding these connections deepens your knowledge.

📝 Create a Formula Sheet

Make your own reference sheet with equations organized by topic. Writing them out helps with memorization and understanding.

About the Author

Adam

Co-Founder @ RevisionTown

Math Expert specializing in various curricula including IB, AP, GCSE, IGCSE, and more