By: Mark C

Date: October 9, 2023

Introduction to Physics Formulas

Physics is the foundational science that explains the nature and properties of matter and energy. It encompasses a variety of fields, including mechanics, thermodynamics, electromagnetism, and quantum mechanics. Understanding physics not only involves grasping complex concepts but also mastering numerous equations and formulas that describe the behavior of our universe. Whether you’re a student preparing for exams or a hobbyist exploring the wonders of physics, having a comprehensive cheat sheet of physics formulas can be immensely helpful.

Mechanics

Newton’s Laws of Motion

• First Law (Inertia): An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.
• Second Law (F=ma): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
• Third Law (Action and Reaction): For every action, there is an equal and opposite reaction.

Kinematics Equations

Kinematics deals with the motion of objects without considering the forces that cause the motion.

• v = u + at – Final velocity (v) is the initial velocity (u) plus acceleration (a) times time (t).
• s = ut + ½at² – Displacement (s) is equal to initial velocity (u) times time (t) plus half of acceleration (a) times time squared.
• v² = u² + 2as – Final velocity squared is the initial velocity squared plus twice the acceleration times displacement.

Dynamics

Gravity

• F = G(m₁m₂/r²) – The gravitational force (F) between two masses (m₁ and m₂) is proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers.

Work and Energy

Work connects force and displacement, while energy relates to the ability to perform work.

• W = Fd cos(θ) – Work (W) is equal to the force (F) multiplied by the displacement (d) and the cosine of the angle (θ) between the force and displacement vectors.
• KE = ½mv² – Kinetic energy (KE) is the energy of motion, equal to half the mass (m) times velocity (v) squared.
• PE = mgh – Potential energy (PE) of an object is its stored energy due to its position, equal to the mass (m) times acceleration due to gravity (g) times height (h).

Thermodynamics

Temperature and Heat

Thermodynamics studies heat, work, and energy on both macroscopic and microscopic levels.

• Q = mcΔT – Heat (Q) added to or removed from a substance results in a change in temperature (ΔT), proportional to its mass (m) and specific heat capacity (c).

First Law of Thermodynamics

The first law is a statement of the conservation of energy principle for thermodynamic systems.

• ΔU = Q – W – The change in internal energy (ΔU) of a system is equal to the heat added to the system (Q), minus the work done by the system (W).

Second Law of Thermodynamics

• No process is possible whose sole result is the transfer of heat from a cooler to a hotter body.
• The total entropy of an isolated system can never decrease over time.

Entropy

• ΔS ≥ 0 – The change in entropy (ΔS) of an isolated system is always greater than or equal to zero.

Electromagnetism

Coulomb’s Law

• F = k(q₁q₂/r²) – The electrostatic force (F) between two charges (q₁ and q₂) is proportional to the product of the charges and inversely proportional to the square of the distance (r) between them, with k being Coulomb’s constant.

Ohm’s Law

• V = IR – Voltage (V) across a resistor is the product of the current (I) through it and its resistance (R).

Faraday’s Law of Electromagnetic Induction

• ε = -dΦ_B/dt – The induced electromotive force (ε) in any closed circuit is equal to the negative of the time rate of change of the magnetic flux (Φ_B) through the circuit.

Maxwell’s Equations

These four partial differential equations form the foundation of classical electrodynamics, optics, and electric circuits.

• Gauss’s Law (Electric): ∮E•dA = Q/ε₀
• Gauss’s Law (Magnetic): ∮B•dA = 0
• Faraday’s Law: ∮E•dl = -dΦ_B/dt
• Ampère-Maxwell Law: ∮B•dl = μ₀I + μ₀ε₀dΦ_E/dt

Optics

Snell’s Law

• n₁sinθ₁ = n₂sinθ₂ – It describes the relationship between the angles of incidence and refraction, when referring to waves passing through a boundary between two different isotropic media.

Lens Formula

• 1/f = 1/do + 1/di – The lens formula relates the focal length (f) of a lens, the object distance (do), and the image distance (di).

Mirror Equation

• 1/f = 1/do + 1/di – Similar to the lens formula, but applicable for mirrors.

Quantum Physics

Planck’s Equation

• E = hf – The energy (E) of a photon is proportional to its frequency (f) with Planck’s constant (h) as the proportionality constant.

Schrödinger Equation

This foundational equation in quantum mechanics describes how the quantum state of a physical system changes over time.

• iħ∂Ψ/∂t = HΨ – Where i is the imaginary unit, ħ is the reduced Planck’s constant, Ψ is the wave function, t is time, and H is the Hamiltonian operator.

Conclusion

Physics formulas are essential tools that enable us to model and comprehend the universe’s phenomena, from the motion of celestial bodies to the behavior of subatomic particles. This ultimate cheat sheet covers the fundamental formulas across various branches of physics, offering a robust reference for learners and professionals alike. By understanding these equations and their applications, you not only prepare yourself for academic success but also empower yourself to explore and innovate in the broader scientific field.