A Comprehensive Guide to Physics Formulas
Physics, the study of matter, energy, and their interactions, is built upon a foundation of fundamental laws and principles. These laws are often expressed mathematically in the form of equations, known as physics formulas. In this article, we'll explore some of the most important physics formulas, categorized by their respective areas of study.
Physical Constants
Speed of Light (c): 3 x 10^8 m/s
Planck's Constant (h): 6.63 x 10^-34 J s
Gravitational Constant (G): 6.67 x 10^-11 N m^2/kg^2
Boltzmann Constant (k): 1.38 x 10^-23 J/K
Avogadro's Number (NA): 6.02 x 10^23 mol^-1
Charge of an Electron (e): 1.6 x 10^-19 C
Permeability of Free Space (μ₀): 4Ï€ x 10^-7 T m/A
Permittivity of Free Space (ε₀): 8.85 x 10^-12 F/m
Coulomb's Constant (k): 9 x 10^9 N m^2/C^2
Faraday Constant (F): 96,485 C/mol
Mass of Electron (me): 9.11 x 10^-31 kg
Mass of Proton (mp): 1.67 x 10^-27 kg
Mass of Neutron (mn): 1.67 x 10^-27 kg
Atomic Mass Unit (u): 1.66 x 10^-27 kg
Stefan-Boltzmann Constant (σ): 5.67 x 10^-8 W/m^2K^4
Rydberg Constant (R): 1.097 x 10^7 m^-1
Bohr Magneton (μB): 9.27 x 10^-24 J/T
Bohr Radius (a₀): 5.29 x 10^-11 m
Standard Atmospheric Pressure (atm): 1.013 x 10^5 Pa
Wien Displacement Constant (b): 2.9 x 10^-3 m K
Laws of Motion
Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with a constant velocity, unless acted upon by an external force.
Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).
Newton's Third Law (Law of Action and Reaction): For every action, there is an equal and opposite reaction.
Work, Power, and Energy
Work (W): The product of force and displacement in the direction of the force (W = Fd cosθ).
Power (P): The rate at which work is done (P = W/t).
Kinetic Energy (KE): The energy of motion (KE = 1/2 mv^2).
Potential Energy (PE): The energy of position or configuration (PE = mgh, PE = 1/2 kx^2).
Work-Energy Theorem: The net work done on an object equals its change in kinetic energy (Wnet = ΔKE).
Conservation of Mechanical Energy: In an isolated system, the total mechanical energy (KE + PE) remains constant.
Center of Mass
Center of Mass (x̄): The point at which the mass of an object is considered to be concentrated (x̄ = Σmixi / Σmi).
Collisions
Conservation of Momentum: In the absence of external forces, the total momentum of a system remains constant (m1u1 + m2u2 = m1v1 + m2v2).
Elastic Collision: Kinetic energy is conserved (1/2 m1u1^2 + 1/2 m2u2^2 = 1/2 m1v1^2 + 1/2 m2v2^2).
Inelastic Collision: Kinetic energy is not conserved; some energy is lost to other forms (e.g., heat, sound).
Rigid Body Dynamics
Angular Velocity (ω): The rate of change of angular displacement (ω = dθ/dt).
Angular Acceleration (α): The rate of change of angular velocity (α = dω/dt).
Torque (τ): The rotational analog of force (τ = Iα).
Rotational Kinetic Energy (Krot): The energy of rotational motion (Krot = 1/2 Iω^2).
Angular Momentum (L): The rotational analog of linear momentum (L = Iω).
Equilibrium
Static Equilibrium: An object is in static equilibrium when the net force and net torque acting on it are both zero (ΣF = 0, Στ = 0).
Kinematics
Equations of Motion:
v = u + at
s = ut + 1/2 at^2
v^2 = u^2 + 2as
Relative Velocity: The velocity of an object relative to another object (vAB = vA - vB).
Projectile Motion: The motion of an object thrown with an initial velocity at an angle to the horizontal.
Vectors
Dot Product: The product of the magnitudes of two vectors and the cosine of the angle between them (A · B = |A||B| cosθ).
Cross Product: The product of the magnitudes of two vectors and the sine of the angle between them, resulting in a vector perpendicular to both (A x B = |A||B| sinθ n).
Note: This article provides a basic overview of some of the most common physics formulas. The actual application of these formulas often involves more complex calculations and considerations.
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