Basic Physics Equations

Complete Guide to Fundamental Physics Formulas

📚 Essential Equations for Physics Students

Understanding Basic Physics Equations

Physics equations are mathematical relationships that describe the fundamental laws of nature. These formulas allow us to predict, calculate, and understand physical phenomena ranging from the motion of objects to the behavior of light and energy. Mastering these basic equations is essential for success in physics courses at all levels.

This comprehensive guide covers the most important physics equations you need to know, organized by topic area. Each formula is presented with its mathematical expression, explanation of variables, and practical applications. Whether you're studying for IB, AP, GCSE, or university-level physics, these equations form the foundation of your physics knowledge.

Understanding when and how to apply these equations is just as important as memorizing them. Throughout this guide, we'll explore the context, units, and real-world applications of each fundamental formula.

Classical Mechanics Equations

Kinematics (Motion)

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 Laws of Motion

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, Energy, and Power

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

Electricity and Magnetism Equations

Electric Circuits

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

Electromagnetism

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

Waves and Optics Equations

Wave Properties

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

Thermodynamics Equations

Heat and Temperature

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

Modern Physics Equations

Quantum and Relativity

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

Important Physical Constants

Speed of Light

\( c = 3.00 \times 10^8 \text{ m/s} \)

Gravitational Acceleration (Earth)

\( g = 9.81 \text{ m/s}^2 \)

Planck's Constant

\( h = 6.626 \times 10^{-34} \text{ J·s} \)

Coulomb's Constant

\( k = 8.99 \times 10^9 \text{ N·m}^2/\text{C}^2 \)

Gas Constant

\( R = 8.314 \text{ J/(mol·K)} \)

Avogadro's Number

\( N_A = 6.022 \times 10^{23} \text{ mol}^{-1} \)

Elementary Charge

\( e = 1.602 \times 10^{-19} \text{ C} \)

Electron Mass

\( m_e = 9.109 \times 10^{-31} \text{ kg} \)

Tips for Mastering Physics Equations

📚 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.