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.
旋轉並縮放一個即時向量，把它拆成水平與垂直分量，並看這些分量如何驅動同一條直線運動與幾何。
Strong first stop for getting into this topic without scanning the whole library.
發射一個拋體，觀察軌跡如何形成，並把射程、最高點與分量運動直接連到發射設定。
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 拋體Group 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.
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.
看單一來源質量如何形成負值的勢阱，比較勢與勢能隨距離的變化，並在同一個即時模型中把 φ 的下降趨勢連到重力場。
比較繞同一來源質量的圓形軌道，理解較大軌道為何需要更長時間：路徑更長、圓周速度更低，而同一個即時模型讓週期定律清楚可見。
Group 04
Stay with force over time, system totals, and collision outcomes without leaving the same mechanics thread.
用定時力脈衝推動小車，觀察動量、衝量與力對時間的面積如何緊扣同一次運動、讀值與圖表。
看兩輛車在同一個受限內部互動中如何交換動量，並理解總動量為何保持不變，而各自速度與質心運動一起更新。
讓兩輛小車在同一條誠實的軌道上碰撞，保持總動量可見，並看彈性、質量與入射速度如何決定反彈或黏在一起的結果。