Motion and kinematics
Kinematics describes where an object is, how quickly its position changes, and how motion evolves with time. The tools separate distance from displacement, speed from velocity, and linear motion from rotation.
Constant velocity and acceleration
Uniform-motion pages connect position, velocity, and time. Constant-acceleration pages add a steady rate of velocity change. If acceleration varies substantially, one constant value cannot represent the interval.
Free fall and projectile paths
Free-fall tools state gravitational acceleration and neglect aerodynamic drag. Projectile pages separate horizontal and vertical components, and distinguish level-ground formulas from horizontal launches above a landing point.
Relative motion and interception
Relative-speed, catch-up, pursuit, and meeting calculations depend on direction. Same-direction speeds are subtracted, while opposing closing speeds are added in a shared reference frame.
Rotation and angular quantities
Period, frequency, angular speed, tangential speed, arc length, angular acceleration, and rotational displacement connect circular motion with linear distance. Radian measure is explicit where the physics requires it.
Stopping and graph interpretation
Stopping tools distinguish reaction travel from braking distance. Graph pages interpret slope on position-time data and signed area under a velocity-time segment.
Forces and free-body models
Newton-law, weight, normal-force, friction, tension, and incline calculators keep the chosen axis visible. Net force is distinguished from any single applied force, and friction coefficients remain tied to the normal reaction used in the model.
Gravity, orbits, and circular motion
Gravitational force, field strength, escape speed, orbital speed, period, altitude, centripetal force, bank angle, and conical-pendulum pages state the radius and central mass assumptions required by their idealized equations.
Torque, machines, and equilibrium
Torque, lever, pulley, moment-balance, center-of-mass, and tipping calculations use signed moments and perpendicular lever arms. Ideal mechanical advantage does not include friction, rope mass, deformation, or machine efficiency.
Stress, strain, and elastic response
Material calculators distinguish force from stress and length change from strain. Young modulus applies to the linear elastic range, while average normal and shear stresses do not represent local stress concentrations.
Energy, work, power, and efficiency
Energy pages distinguish kinetic, gravitational, and spring energy while work pages retain force direction and displacement. Power describes an energy-transfer rate, and efficiency compares useful output with the full input on the same energy basis.
Momentum, impulse, collisions, and rockets
Momentum tools keep velocity signs explicit through impulses, sticking collisions, elastic impacts, restitution, recoil, ballistic pendulums, and the ideal rocket equation. System boundaries and external impulses determine when conservation applies.
Rotational energy and inertia
Angular momentum, standard moments of inertia, torque-driven acceleration, rotational power, rolling, flywheels, shifted axes, gyration radius, precession, pendulums, and spring oscillations retain the specified axis and ideal-body assumptions.
Fluid properties, pressure, and buoyancy
Density and specific gravity connect mass with occupied volume. Pressure pages distinguish force per area, gauge pressure, and absolute pressure, while buoyancy and hydraulic tools retain the displaced volume or piston-area relationship that makes the model work.
Flow, viscosity, and drag
Continuity, Bernoulli, tank outflow, Reynolds number, Poiseuille flow, settling, and drag calculations state their geometry and flow assumptions. Viscosity, temperature, pipe diameter, and reference area can change a result sharply and should remain attached to it.
Wave relationships and resonances
Wave speed, frequency, wavelength, period, angular frequency, wave number, string tension, and fundamental modes describe different parts of a repeating disturbance. Boundary conditions and the medium determine which resonance equation applies.
Sound levels, resonance, and Doppler shift
Acoustic pages separate linear intensity from logarithmic level, one-way distance from echo travel, and source motion from observer motion. Resonance tools state whether a pipe is open or closed and which harmonic numbers its boundaries permit.
Refraction, lenses, and interference
Optics calculators retain angle-from-normal and distance sign conventions through refraction, critical angle, lenses, mirrors, power, diffraction, and double-slit patterns. Paraxial or small-angle assumptions remain visible where they control the result.
Thermal expansion and heat transfer
Expansion, restrained stress, conduction, resistance, radiation, blackbody peaks, heat engines, and refrigeration pages keep absolute temperatures distinct from temperature differences and state the material or reservoir model.
Photons, matter waves, and relativity
Modern-physics tools connect photon energy and wavelength, nonrelativistic matter waves, and special-relativistic frame comparisons. Constants, proper quantities, subluminal domains, and motion direction remain explicit.
Model limits
These are transparent educational models. Real motion can include drag, slope, changing acceleration, traction limits, uncertainty, and three-dimensional paths. Safety-critical decisions require verified measurements and suitable professional methods.