Use vectors, balance and rotational cause, angular momentum, trajectories, gravity fields and potential, circular orbits, orbital periods, escape thresholds, impulse, conservation, and collisions to read motion and interactions on the same simulation-first surface.
Mechanics is the place to start when you want the language of motion, then the interactions that change that motion. The page stays compact by grouping the catalog into motion-reading ideas, one bounded rotational branch that now includes torque, static equilibrium / centre of mass, rotational inertia, rolling motion, and angular momentum, one bounded gravity bridge that now includes field, energy, orbital-speed, orbital-period, and escape-threshold views, and momentum-driven interactions instead of making you scan every module cold.
Best first concepts
The topic page keeps these starts in their own compact row so the first screen is about orientation and next action, not stacked feature cards.
Rotate and scale a live vector, decompose it into horizontal and vertical parts, and watch those components drive the same straight-line motion and geometry.
Vector foundations
Strong first stop for getting into this topic without scanning the whole library.
Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.
Two-dimensional motion
Strong first stop for getting into this topic without scanning the whole library.
Related guided tracks
These tracks stay tied to the same shared concept pages and progress model. They are surfaced here either because the authored path meaningfully overlaps this topic page or because the topic catalog marks the track as useful preparation for this branch.
Start with torque as the turning effect of force, use centre of mass and support region for static balance, then carry the same rotational language into moment of inertia, rolling motion, and angular momentum.
Track progress
0 / 8 moments complete
0 / 5 concepts and 0 / 3 checkpoints cleared.
Torque opens this track and sets up the rest of the path.
Start with vector components, move into projectile paths, and then use circular motion to understand how velocity can keep changing direction.
Track progress
0 / 5 moments complete
0 / 3 concepts and 0 / 2 checkpoints cleared.
Vectors and Components opens this track and sets up the rest of the path.
Start with one source mass creating a field and potential well, then use that same gravity model to explain circular speed, orbital periods, and the escape threshold.
Track progress
0 / 8 moments complete
0 / 5 concepts and 0 / 3 checkpoints cleared.
Gravitational Fields opens this track and sets up the rest of the path.
Grouped concept overview
Each group is authored in the topic catalog, but the actual concepts, progress badges, and track cues still come from the canonical concept metadata and shared progress model.
Group 01
Build the coordinate and component language first, then use it in a live projectile path.
Rotate and scale a live vector, decompose it into horizontal and vertical parts, and watch those components drive the same straight-line motion and geometry.
Vector foundations
Strong first stop for getting into this topic without scanning the whole library.
Built for quick scanning, filtering, and direct access.
Open conceptLaunch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.
Two-dimensional motion
Strong first stop for getting into this topic without scanning the whole library.
Strong first module for getting into the public preview.
Open conceptGroup 02
Stay with one compact rotational branch: first use a pivoted bar to make rotational cause visible, then let centre of mass and support region turn that same torque language into static balance, next keep the mass-distribution story for spin-up resistance, then let rolling motion tie translation and rotation together on one incline, and finally treat angular momentum as the conserved rotational analogue of momentum.
Push on one pivoted bar and see how lever arm distance, force direction, and turning effect stay tied to the same compact rotational bench.
Turning effects of force
Built for quick scanning, filtering, and direct access.
Open conceptShift one support region under one loaded plank and see how centre of mass, support reactions, and torque balance decide whether the object stays stable or tips.
Balance, support, and centre of mass
Built for quick scanning, filtering, and direct access.
Open conceptKeep the same total mass and torque, then slide equal masses inward or outward to see why moment of inertia makes some rotors much harder to spin up than others.
Mass distribution and rotational response
Built for quick scanning, filtering, and direct access.
Open conceptRoll a sphere, cylinder, hoop, or custom mass distribution down one incline and see how rolling without slipping ties translation, rotation, and rotational inertia to the same honest run.
Rolling without slipping
Built for quick scanning, filtering, and direct access.
Open conceptTreat angular momentum as rotational momentum on one compact rotor where mass radius and spin rate stay tied to the same readouts, response maps, and same-L conservation story.
Rotational momentum and conservation
Built for quick scanning, filtering, and direct access.
Open conceptGroup 03
Use one bounded source-mass model to connect inward pull, potential-well depth, circular-orbit balance, the period law for larger and smaller circular years, and the later escape-threshold question without leaving the same gravity thread.
See how one source mass creates an inward gravitational field, how source mass and distance set the field strength, and how a probe mass turns that field into force without changing the field itself.
Gravity and orbit bridges
Built for quick scanning, filtering, and direct access.
Open conceptSee one source mass create a negative potential well, compare how potential and potential energy change with distance, and connect the downhill slope of phi to the gravitational field on the same live model.
Gravity and orbit bridges
Built for quick scanning, filtering, and direct access.
Open conceptSee why a circular orbit needs the right sideways speed, how gravity supplies the centripetal acceleration, and how source mass and radius together set orbital speed and period on one bounded live model.
Gravity and orbit bridges
Built for quick scanning, filtering, and direct access.
Open conceptCompare circular orbits around one source mass and see why larger orbits take longer: the path is longer, the circular speed is lower, and the same live model makes the period law visible without hiding the gravity-speed link.
Gravity and orbit bridges
Built for quick scanning, filtering, and direct access.
Open conceptLaunch outward from one bounded gravity source and see how source mass, launch radius, and total specific energy decide whether the object escapes or eventually returns.
Gravity and orbit bridges
Built for quick scanning, filtering, and direct access.
Open conceptGroup 04
Stay with force over time, system totals, and collision outcomes without leaving the same mechanics thread.
Push one cart with a timed force pulse and watch momentum, impulse, and force-time area stay tied to the same motion, readouts, and graphs.
Momentum and force over time
Built for quick scanning, filtering, and direct access.
Open conceptWatch two carts trade momentum through one bounded internal interaction and see the total stay fixed while the individual momenta, velocities, and center-of-mass motion update together.
Multi-object interactions
Built for quick scanning, filtering, and direct access.
Open conceptCollide two carts on one honest track, keep total momentum in view, and see how elasticity, mass, and incoming speed shape the rebound or stick-together outcome.
Collisions and restitution
Built for quick scanning, filtering, and direct access.
Open concept