Neutron STEM Lab

Mechanics Workbench

Fifteen mechanics calculators and simulations covering motion, forces, energy, rotation, oscillations, and gravity.

Mechanics: labelled diagrams and key equations for mechanics, kinematics, forces, and energy.
Browser-local interactive workspace
Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Mechanics: theory, method, and sources

This physics workspace publishes 13 governing equations, 6 stated assumptions, 3 documented boundaries, and 1 source so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

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.

Calculators and topics covered

  • mechanics
  • kinematics
  • forces
  • energy
  • momentum
  • rotation
  • oscillation
  • gravity
  • kinematics calculator
  • projectile motion simulator
  • newtons second law calculator
  • work energy power calculator
  • momentum collision calculator
  • circular motion calculator

Core equations

kinematics:vf=vi+at  and  Δx=vi  t+12at2\text{kinematics:}\quad v_{f} = v_{i} + at\; and\; \Delta x = v_{i}\; t + \frac{1}{2} at^{2}projectiles:x=v0  cos⁡(θ)t  and  y=h0+v0  sin⁡(θ)t−12gt2\text{projectiles:}\quad x = v_{0}\; \cos \left(\theta \right) t\; and\; y = h_{0} + v_{0}\; \sin \left(\theta \right) t - \frac{1}{2} gt^{2}Newton’s second law:Fnet=ma\text{Newton’s second law:}\quad F_{\mathrm{net}} = maenergy:KE=12mv2,  PE=mgh,  W=Fd  cos⁡  θ,  P=Wt\text{energy:}\quad \mathrm{KE} = \frac{1}{2} mv^{2},\; \mathrm{PE} = mgh,\; \mathrm{W} = Fd\; \cos \; \theta ,\; P = \frac{\mathrm{W}}{t}momentum conservation:∑pbefore=∑pafter\text{momentum conservation:}\quad \sum p_{\mathrm{before}} = \sum p_{\mathrm{after}}circular motion:ac=v2r  and  Fc=mv2r\text{circular motion:}\quad a_{c} = \frac{v^{2}}{r}\; and\; F_{c} = \frac{mv^{2}}{r}torque and rotation:τ=rF  sin⁡  θ,  α=τI,  KErot=12Iω2\text{torque and rotation:}\quad \tau = rF\; \sin \; \theta ,\; \alpha = \frac{\tau }{I},\; \mathrm{KE}_{\mathrm{rot}} = \frac{1}{2} I\omega ^{2}friction:fs,max=μsN  and  fk=μkN\text{friction:}\quad f_{\mathrm{s,max}} = \mu _{s} N\; and\; f_{k} = \mu _{k} Ncenter of mass:rcm=∑miri∑mi\text{center of mass:}\quad r_{cm} = \frac{\sum m_{i} r_{i}}{\sum m_{i}}pendulum:T≈2πLg\text{pendulum:}\quad T \approx 2 \pi \sqrt{\frac{L}{g}}spring and SHM:F=−kx  and  ω=km\text{spring and SHM:}\quad F = - kx\; and\; \omega = \sqrt{\frac{k}{m}}gravitation:F=Gm1m2r2\text{gravitation:}\quad F = \frac{Gm_{1} m_{2}}{r^{2}}escape velocity:vesc=2GMr\text{escape velocity:}\quad v_{\mathrm{esc}} = \sqrt{\frac{2 GM}{r}}

Method and assumptions

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 and design boundaries

  • 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.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy
  • Classical mechanics relationshipsThe workbench implements the conventional Newtonian mechanics equations listed above.

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Projectile Motion Calculator

Calculate projectile flight time, range, maximum height, launch components, and impact speed without aerodynamic drag.