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.
Specific learning goals
These goal cards stay authored and transparent. They reuse the current topic page, starter tracks, guided collections, concept bundles, and progress cues instead of adding a separate recommendation system on top of this branch.
Use the vectors topic route, the new bridge collection, the short bridge track, and the mechanics topic page so vectors feel like one language before motion problems take over.
Primary move
Open topic route
No saved progress yet inside Vectors.
Entry diagnostic
Start from the opening step
No saved diagnostic checks are available yet, so the opening step is still the best entry into the collection.
Reuses the guided collection entry for Vectors to Mechanics Bridge, with 0 of 3 probes already ready.
No saved progress yet inside Vectors.
Open the vectors topic route is the next guided collection step.
Vectors in 2D opens this track and sets up the rest of the path.
No saved progress yet inside Mechanics.
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.
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.
Strong first stop for getting into this topic without scanning the whole library.
A strong first concept for opening the catalog without committing to a full track.
Open ProjectileGroup 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.
Shift 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.
Keep 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.
Roll 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.
Treat 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.
Group 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.
See 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.
See 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.
Compare 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.
Launch 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.
Group 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.
Watch 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.
Collide 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.