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39 results for "Vectors".
Topic results
5 resultsVectors
Use one 2D plane to read vectors as arrows, ordered pairs, matrix actions, alignment measures, and projections before the same language bridges into motion.
Math3 concepts
Open VectorsMechanics
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.
Physics15 concepts
Open MechanicsFunctions
Use parent-curve moves, a shifted reciprocal family, and one exponential bench so graph moves, asymptotes, domain breaks, growth versus decay, and target-time questions stay tied to the same visual branch before the math path widens into local and accumulated change.
Math3 concepts
Open FunctionsCalculus
Start from slope on the graph itself, use one constrained rectangle bench to make a real maximum visible, keep limit and continuity behavior available on one target point, and then widen into signed area and accumulation so rate and total change stay connected on one visual branch.
Math4 concepts
Open CalculusComplex Numbers and Parametric Motion
Use one bounded math branch where the complex plane, unit-circle rotation, polar coordinates, trig identities, inverse-angle reasoning, and motion traced from equations all stay tied to the same coordinate language.
Math6 concepts
Open Complex Numbers and Parametric MotionConcept results
25 resultsVectors and Components
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.
PhysicsMechanics
Open VectorsVectors in 2D
Combine, subtract, and scale vectors on one plane so magnitude, direction, and components stay tied to the same live object.
MathVectors
Open 2D vectorsUniform Circular Motion
Track a particle moving at constant speed around a circle and connect radius, angular speed, tangential speed, centripetal acceleration, and the inward-force requirement to the same live state.
PhysicsOscillations and Waves
Open UCMMatrix Transformations / Stretch, Shear, Reflection
Let one 2 by 2 matrix act on a grid, the basis vectors, and a sample shape so stretch, shear, reflection, and combined plane changes stay visual instead of symbolic-only.
MathVectors
Open Matrix transformsDot Product / Angle and Projection
Keep two vectors, their angle, the signed projection of one onto the other, and the dot product visible together so alignment reads geometrically instead of as memorized cases.
MathVectors
Open Dot productComplex Numbers on the Plane
Read complex numbers as points and vectors on one plane, then keep addition and multiplication geometric instead of symbolic-only.
MathComplex Numbers and Parametric Motion
Open Complex numbersTorque
Push on one pivoted bar and see how lever arm distance, force direction, and turning effect stay tied to the same compact rotational bench.
PhysicsMechanics
Open TorqueStatic Equilibrium / Centre of Mass
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.
PhysicsMechanics
Open Static equilibriumRotational Inertia / Moment of Inertia
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.
PhysicsMechanics
Open Rotational inertiaRolling Motion
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.
PhysicsMechanics
Open Rolling motionAngular Momentum
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.
PhysicsMechanics
Open Angular momentumMomentum and Impulse
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.
PhysicsMechanics
Open Momentum / ImpulseConservation of Momentum
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.
PhysicsMechanics
Open Momentum conservationCollisions
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.
PhysicsMechanics
Open CollisionsProjectile Motion
Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.
PhysicsMechanics
Open ProjectileGravitational Fields
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.
PhysicsMechanics
Open Gravity fieldsGravitational Potential and Potential Energy
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.
PhysicsMechanics
Open Gravity potentialCircular Orbits and Orbital Speed
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.
PhysicsMechanics
Open Orbital speedKepler's Third Law and Orbital Periods
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.
PhysicsMechanics
Open Orbital periodsEscape Velocity
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.
PhysicsMechanics
Open Escape speedUnit Circle / Sine and Cosine from Rotation
Keep one rotating point, its x and y projections, and the sine-cosine traces linked so the unit circle becomes the live source of both functions.
MathComplex Numbers and Parametric Motion
Open Unit circle rotationPolar Coordinates / Radius and Angle
Keep one point visible in polar and Cartesian views at the same time so radius and angle turn directly into x and y on the plane.
MathComplex Numbers and Parametric Motion
Open Polar coordinatesParametric Curves / Motion from Equations
Keep x(t), y(t), the traced path, and the moving point visible together so shape and traversal stay distinct.
MathComplex Numbers and Parametric Motion
Open Parametric curvesTrig Identities from Unit-Circle Geometry
Keep one rotating point and its projections visible so the core trig identities stay tied to geometry instead of detached symbol rules.
MathComplex Numbers and Parametric Motion
Open Trig identitiesInverse Trig / Angle from Ratio
Keep one polar point and its coordinate signs visible so inverse trig becomes angle-from-ratio reasoning with quadrant checks instead of a calculator-only output.
MathComplex Numbers and Parametric Motion
Open Inverse trigStarter track results
3 resultsVectors and Motion Bridge
Start with vectors as geometric objects on a 2D plane, then carry the same component language into the existing motion-facing vectors bench.
Math2 concepts
Open Vectors and Motion BridgeMotion and Circular Motion
Start with vector components, move into projectile paths, and then use circular motion to understand how velocity can keep changing direction.
Physics3 concepts
Open Motion and Circular MotionComplex and Parametric Motion
Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).
Math6 concepts
Open Complex and Parametric MotionGuided collection results
2 resultsVectors to Mechanics Bridge
Use the vectors topic route, the short bridge track, one endpoint checkpoint, and the mechanics topic route so the math-to-motion handoff stays compact and teacher-usable.
MathLesson set
Open lesson setComplex and Parametric Motion Lesson Set
Use the complex-and-parametric topic route, the authored starter track, one parametric-motion checkpoint, and the vectors topic route so the plane-based math branch stays compact and teacher-usable.
MathLesson set
Open lesson setGoal path results
2 resultsBridge plane vectors into motion
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.
MathPrepare for a branch
Open goal pathBuild plane intuition through complex numbers and parametric motion
Use the complex-and-parametric topic route, the new lesson set, the compact starter track, and the vectors topic page so the plane language widens from complex numbers into unit-circle and polar-coordinate geometry, then deepens into trig identities and inverse-angle reasoning before motion.
MathBuild intuition
Open goal pathSubject results
2 resultsPhysics
Enter the current physics catalog through live motion, waves, fields, circuits, and modern-physics benches that still share one compact simulation-first product language.
Physics8 topics
Open PhysicsMath
Enter the current math slice through graph transformations, rational-function asymptotes, exponential change, vectors, complex-plane geometry, trig identities, inverse-angle reasoning, polar coordinates, and parametric motion without leaving the same live-bench product language used elsewhere on the site.
Math4 topics
Open Math