Category
Physics
Physics calculators for classical mechanics, kinetic energy, Hooke's law elasticity, gravitational force, centripetal motion, and ideal gas states.
STEM Topic Hub
Understanding Physics
Core concepts, governing principles, and contextual organization in physics.
Physics explores the fundamental laws governing energy, matter, force, and motion. DudeMath provides computational models for classical Newtonian mechanics, work-energy theorems, orbital gravitation, harmonic oscillation, and thermodynamics.
Core Governing Concepts & Formulas
Work & Kinetic Energy
KE = 0.5 × m × v², W = F × d × cos(θ) Mechanical energy transfer and translational kinetic energy.
Forces & Dynamics
F_net = m × a, F_c = (m × v²) / r, F_g = G(m₁m₂) / r² Newtonian vector forces, centripetal acceleration, and universal gravitation.
Thermodynamics & Elasticity
P × V = n × R × T, F = -k × x Ideal gas equation of state and linear Hookean elastic restoring forces.
Recommended Learning & Calculation Workflow
Core Theory Guides & Foundational Reference
Kinetic Energy & Work Theorem
Work-energy equivalence, quadratic velocity scaling, and braking stopping distance.
2D Projectile Trajectory Kinematics
Orthogonal velocity vector decomposition, parabolic trajectory range, and apex flight time.
Centripetal Radial Acceleration
Inward kinematic acceleration requirement and real constraint forces in circular motion.
Ideal Gas Law Equation of State
Thermodynamic state relation PV = nRT, absolute Kelvin scaling, and gas density.
Simple Harmonic Pendulum Period
Small-amplitude period formulation, mass independence, and square-root length scaling.
Hooke's Law & Elastic Restoring Force
Linear elastic spring stiffness, displacement measurement, and proportional yield limits.
Coulomb Friction & Incline Normal Force
Static limit vs kinetic sliding friction and incline normal contact force.
Newton's Universal Gravitation
Inverse-square law, center-to-center mass separation, and orbital attraction.
Scope & Limitations: Models assume classical non-relativistic kinematics (v ≪ c) and idealized conditions (e.g. frictionless streamlines, point-mass pendulums at small angular displacements θ < 15°).
Topic Clusters
Calculators by Topic
Calculators grouped by their specific engineering or mathematical focus area.
Work & Kinetic Energy
Kinetic energy KE = 1/2 mv² and mechanical work W = F · d · cos(θ).
Kinetic Energy Calculator: KE = ½mv² in Joules | DudeMath
Calculate translational kinetic energy in Joules using KE = ½mv² from mass and velocity. Includes velocity conversions and step-by-step calculations.
Work Done Calculator: W = F·d·cos(θ) in Joules | DudeMath
Calculate mechanical work done in Joules using W = F·d·cos(θ). Features force, displacement distance, angle components, and work-energy theorem steps.
Forces & Trajectory Dynamics
Centripetal force, frictional opposition, universal gravitation, and projectile ballistics.
Centripetal Force Calculator: Fc = mv²/r & Accel | DudeMath
Calculate circular motion centripetal force (Fc = mv²/r) and centripetal acceleration (ac = v²/r) from mass, linear velocity, and path curve radius.
Friction Force Calculator: Ff = μ·Fn Friction | DudeMath
Calculate limiting friction force using the Amontons-Coulomb law (Ff = μ·Fn) and determine the angle of repose from the friction coefficient directly.
Gravitational Force Calculator: F = G·m₁m₂/r² | DudeMath
Calculate Newton's universal gravitational attraction (F = G·m₁m₂/r²) between two point masses and circular orbital speed using standard SI units.
Projectile Motion Calculator: Range & Trajectory | DudeMath
Calculate parabolic trajectory, maximum flight height, time of flight, and horizontal range using kinematic equations. Instant launch angle solutions.
Harmonic Oscillation & Pendulums
Simple pendulum period T = 2π√(L/g) and harmonic restoring dynamics.
Thermodynamics & Ideal Gases
Ideal gas equation of state PV = nRT relating pressure, volume, temperature, and molar quantity.
Linear Elasticity & Springs
Hooke's law F = k · x and linear restoring spring stiffness.