Mechanics Workbench
Fifteen mechanics calculators and simulations covering motion, forces, energy, rotation, oscillations, and gravity.
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How this tool works
The Mechanics Workbench separates mechanics from waves and thermodynamics so each physics area can expand independently.
It includes fifteen focused modules with SI-unit inputs, calculated intermediate quantities, and dynamic diagrams for the visual models.
Core equations
kinematics: v_f = v_i + at and Δx = v_i t + ½at²projectiles: x = v₀ cos(θ)t and y = h₀ + v₀ sin(θ)t − ½gt²Newton’s second law: F_net = maenergy: KE = ½mv², PE = mgh, W = Fd cos θ, P = W/tmomentum conservation: Σp_before = Σp_aftercircular motion: a_c = v²/r and F_c = mv²/rtorque and rotation: τ = rF sin θ, α = τ/I, KE_rot = ½Iω²friction: f_s,max = μ_sN and f_k = μ_kNcenter of mass: r_cm = Σmᵢrᵢ / Σmᵢpendulum: T ≈ 2π√(L/g)spring and SHM: F = −kx and ω = √(k/m)gravitation: F = Gm₁m₂/r²escape velocity: v_esc = √(2GM/r)Assumptions
- Inputs use SI units unless the field explicitly displays another unit.
- Projectile motion neglects aerodynamic drag and uses uniform gravitational acceleration.
- Collision models are one-dimensional and isolated from external impulse.
- The pendulum simulator uses the small-angle harmonic approximation.
- Spring and SHM models use an ideal massless spring without damping.
- Escape velocity neglects atmosphere, rotation, propulsion losses, and other bodies.
Limitations
- The tools provide educational and preliminary analytical models rather than safety-critical engineering validation.
- Static and kinetic friction coefficients must be selected for the actual material pair and conditions.
- Large-angle pendulum motion and damped or driven oscillations require more advanced numerical models.
References and verification
- Classical mechanics relationshipsThe workbench implements the conventional Newtonian mechanics equations listed above.