Domain
Engineering Mechanics
Engineering Mechanics on Anemodia: statics and equilibrium, mass properties (centroid, second moment of area, parallel-axis theorem, centre of mass), particle mechanics, rigid-body mechanics and vibrations.
Every tool below is solved by the same typed Mechanics computation modules, so a calculator and the Lab it hands off to can never disagree. Calculators answer one well-posed question; Labs keep a whole model on screen — geometry, loads, diagrams and derived quantities together.
Statics & Equilibrium
Planar force systems, resultants, moments, rigid-body support reactions and dry static friction.
- Resultant Force CalculatorVector sum of coplanar forces: resultant components, magnitude and direction, with the zero-resultant case reported honestly.
- Moment of a Force CalculatorMoment of a planar force about a chosen point, M = r × F, positive counter-clockwise, with the perpendicular lever arm.
- 2D Equilibrium CalculatorSupport reactions of a planar rigid body from ΣFx = 0, ΣFy = 0 and ΣM = 0, with an explicit determinate, indeterminate or inconsistent verdict.
- Static Friction CalculatorMaximum static friction μs·N against the required equilibrium force, distinguishing sticking, impending slip and no static equilibrium.
Mass Properties
Centroid, centre of mass, second moment of area (area moment of inertia), the parallel-axis theorem, radius of gyration and mass moment of inertia.
- Centroid CalculatorArea and geometric centroid of a single shape or a composite section, with cutouts as negative signed areas.
- Center of Mass CalculatorTotal mass and centre of mass of discrete planar point masses, or of a composite body built from shapes with densities, with each contribution shown.
- Area Moment of Inertia CalculatorCentroidal Ix, Iy and Ixy in m⁴ for standard shapes, with parallel-axis translation and principal values.
- Mass Moment of Inertia CalculatorMass moment of inertia in kg·m² for standard rigid bodies, with the axis stated for every case.
- Huygens–Steiner (Parallel-Axis) Theorem CalculatorTransfer a centroidal inertia to a parallel axis with the Huygens–Steiner theorem, also known as the parallel-axis theorem, in the area form I_c + A·d² or the mass form I_G + m·d².
- Radius of Gyration CalculatorRadius of gyration k = √(I/A) for an area or k = √(I/m) for a mass, undefined when the divisor is not positive.
Particle Mechanics
Constant-acceleration and curvilinear motion, projectile motion, circular motion, ΣF = m·a, work–energy, impulse–momentum and collisions.
- Constant Acceleration CalculatorExact constant-acceleration kinematics: the standard 1D relations with explicit solve modes, and 2D propagation of position, velocity and speed.
- Projectile Motion CalculatorIdeal projectile motion: launch components, apex, flight time to a chosen landing elevation, range, impact velocity and impact angle.
- Circular Motion CalculatorParticle circular motion: v = rω, normal and tangential acceleration, total acceleration, period, frequency and the vectors at a chosen angle.
- Newton's Second Law CalculatorΣF = m·a for a planar particle, with explicit modes for the resultant force, the mass or the acceleration from several known forces.
- Work–Energy CalculatorWork of a constant force, particle kinetic energy and the work–energy theorem, with an honest verdict when no physical final speed exists.
- Impulse–Momentum CalculatorPlanar impulse and linear momentum: p = m·v, J = F·Δt and J = Δp, kept as distinct quantities throughout.
- Collision CalculatorDirect 1D impact of two particles from momentum conservation and the coefficient of restitution, with the kinetic-energy loss.
- Curvilinear Motion CalculatorPlanar curvilinear kinematics in normal–tangential or polar coordinates, with the components, the total acceleration and the Coriolis-like polar term named explicitly.
Rigid-Body Mechanics
Rotational kinematics, rolling without slipping, planar equations of motion, rigid-body work–energy and impulse–momentum.
Rigid-Body Kinematics
availablePlanar translation, rotation and general plane motion: the velocity and acceleration of body-fixed points and the instantaneous centre of zero velocity.
Engineering Mechanics
Open Lab →
Rigid-Body Dynamics
availablePlanar kinetics under global forces at body-fixed points: load reduction, ΣF = m·a_G and ΣM_G = I_G·α, the resulting motion, energy and momentum.
Engineering Mechanics
Open Lab →
- Rotational Kinematics CalculatorConstant angular-acceleration relations between θ, ω, α and t, with one explicit unknown per mode.
- Rotational Dynamics CalculatorΣM_G = I_G·α for a planar rigid body, solved for the moment, the mass moment of inertia or the angular acceleration.
- Rigid-Body Work–Energy CalculatorT = ½m|v_G|² + ½I_Gω² with the translational and rotational parts kept apart, and T₂ − T₁ = W_net solved either way.
- Rigid-Body Impulse–Momentum CalculatorJ = m(v_G2 − v_G1) and K_G = I_G(ω₂ − ω₁) for one planar rigid body, including constant loads acting over a duration.
- Rolling Without Slipping CalculatorPure-rolling kinematics with the contact and top point velocities, and the incline case with the static friction the no-slip constraint demands.
Dynamics & Vibrations
Free and forced vibration of mechanical systems, resonance and isolation, natural frequencies and mode shapes.
Vibrations (Mass–Spring–Damper)
availableFree, forced, harmonic and base-excited single-degree-of-freedom vibration: resonance, transmissibility, isolation and energy.
Dynamics & Control · Engineering Mechanics
Open Lab →
Modal Analysis (2DOF & MDOF)
availableNatural frequencies, mode shapes, orthogonality, Rayleigh and modal damping, modal superposition, participation factors and receptance FRFs for M q̈ + C q̇ + K q = f(t).
Dynamics & Control · Engineering Mechanics
Open Lab →