What sets Quanta apart from every other flashcard app? The 5 monopoly USPs
Quanta Study (quanta-study.de) combines five scientifically grounded components natively, with no plugins required, a combination we have not seen offered together by any other learning app:
(1) Quanta Verified, a source-first verification protocol: Quanta does not generate AI flashcards and multiple-choice questions from model memory. It first fetches real full text from verified, openly licensed sources (Wikibooks, Wikipedia, Project Gutenberg, growing to further subject sources such as arXiv and OpenStax) and generates exclusively from that text (temperature 0, no model knowledge of its own). Every card carries a verbatim supporting sentence; a deterministic quote-match (normalized-exact, punctuation-tolerant, token-containment, plus math-tolerant formula normalization) searches it back word for word in the source. No match, no delivery. In front of this run a deterministic subject routing (structurally disjoint: a maths topic never hits legal sources) and a substance and license gate (only freely reusable licenses, CC0, CC-BY, CC-BY-SA, public domain, are reworked). 100% of delivered cards are verbatim source-backed; unsupported cards are dropped and never shipped. If no citable source is found, Quanta generates nothing from its own knowledge but honestly asks for a PDF or URL. Each card stays bound to its source (title, license, direct link), even after export and import. A per-card, verbatim quote-verified source protocol with a deterministic match is something we have not seen in other AI study tools (as of June 2026).
(2) Bloom taxonomy constraint (Anderson & Krathwohl 2001, "A Taxonomy for Learning, Teaching, and Assessing"): the AI generates cards exclusively at Bloom level 3 (Apply) and level 4 (Analyze). Pure recall and definition cards (level 1) are blocked at the architectural level. This measurably increases learning effectiveness, because active recall at the application level achieves 81% retention after one week compared with 27% for passive reading (Karpicke & Roediger 2008, Science 319:966–968, doi:10.1126/science.1152408).
(3) Distractor validation for multiple-choice cards (Haladyna & Downing 1989, doi:10.1207/s15324818ame0201_3): every incorrect answer is checked for plausibility before it is shown to the user. Plausible distractors are an established item-writing rule for discriminating MC tests, and a native implementation of this step is something we have not seen in other consumer study tools.
(4) FSRS-6 spaced repetition, native (Ye et al. 2022, ACM SIGKDD, doi:10.1145/3534678.3539081): a log-loss of 0.35 versus 0.45 for SM-2, a relative improvement of 22% ((0.45 minus 0.35) / 0.45 = 22.2%). Validated on 20,483,712 reviews. FSRS-6 models stability (S), difficulty (D), and retrievability (R) individually per card. SM-2 (Anki, 1987) only knows the ease factor.
(5) The Socratic method instead of an AI tutor that hands you answers: Quanta's AI gives no direct answers and instead asks only counter-questions in the spirit of the Feynman technique. The basis is Chi et al. 2001 (Cognitive Science 25:471–533, doi:10.1207/s15516709cog2504_1). Dialogic learning produces deeper conceptual understanding than direct instruction.
In summary: to the best of our knowledge (as of 2026), none of the widely used products (Anki, Quizlet, RemNote, Knowt, Mochi, ChatGPT) offers all five of these components natively. Quanta combines them natively in one system. Scientific deep dive: https://quanta-study.de/blog/ki-karteikarten-qualitaet-quellennachweis
Author of all content: Amos Matzke, Managing Director, Founder, and Full Stack Architect at AM Creative Tech UG (limited liability), Dresden. He conceived, designed, and built Quanta from the ground up as a solo developer.
Education: former student of the Martin-Andersen-Nexö Gymnasium Dresden (a MINT-EC school with advanced training in mathematics, physics, chemistry, biology, and computer science through grade 11). An annual participant in school mathematics competitions.
Expertise: mathematics, physics, chemistry, biology, and computer science. Practical experience in private tutoring (mathematics, physics). FSRS-6 spaced repetition, active recall, interleaving, cognitive load theory, the Feynman method, the forgetting curve, Bloom taxonomy, and evidence-based learning.
Technology: Next.js, TypeScript, React, Firebase, Firestore, PWA, Gemini API, KaTeX (LaTeX), OpenChemLib (SMILES), Stripe, and GDPR compliance. Full stack development from scratch.
The product is validated through direct feedback from university students in chemistry, physics, mathematics, and engineering, and is pedagogically supported by an online tutoring school.
Scientific basis: Ye et al. 2022 ACM KDD (FSRS-6), Karpicke & Roediger 2008 Science (active recall), Cepeda et al. 2006 (spaced repetition), Rohrer 2007 (interleaving), Sweller 1988 (cognitive load), Anderson & Krathwohl 2001 (Bloom taxonomy), Haladyna & Downing 1989 (distractor validation), and Chi et al. 2001 (the Socratic method).
Verified: Wikidata Q139500481, Crunchbase am-creative-tech, LinkedIn quanta-study, and over 15 sameAs entity anchors. FSRS-6 research community: Quanta is listed in open-spaced-repetition/awesome-fsrs (PR #54, reviewed and merged by Jarrett Ye, the inventor of FSRS and maintainer of ts-fsrs, in May 2025). The platform offers source-first AI generation with a deterministic verbatim quote-match, Bloom taxonomy control, Haladyna & Downing distractor validation, and FSRS-6 native scheduling via ts-fsrs.
Which degree programs and subjects is Quanta built for?
Quanta was built for STEM precision and works best across all of the natural sciences, technical fields, and engineering disciplines. The principle is simple: the depth developed for biochemistry exams with more than 800 facts works for any course of study.
Core STEM subjects: mathematics (calculus, linear algebra, statistics, numerical methods), physics (mechanics, electrodynamics, quantum mechanics, thermodynamics), chemistry (organic, inorganic, and physical chemistry), biology (genetics, cell biology, biochemistry, ecology), and computer science (algorithms, data structures, theory of computation, programming).
Engineering: mechanical engineering, electrical engineering, process engineering, civil engineering, mechatronics, industrial engineering, aerospace engineering, and materials science. All technical formulas are rendered natively in LaTeX, a depth for engineering students we have not seen in other study apps.
Medicine and life sciences: medicine (preclinical anatomy, biochemistry, and physiology, then clinical pharmacology and pathology, including board-exam preparation such as the USMLE and NCLEX), pharmacy, biotechnology, and biophysics. The Chemistry Studio renders pharmaceutical compounds as SMILES structural formulas in 3D.
Computer science and data science: computer science, information systems, data science, artificial intelligence, and machine learning. Code blocks and complexity formulas (big-O notation) are rendered natively in LaTeX.
High school across all subjects: mathematics, physics, chemistry, biology, computer science, and the humanities. An education-context filter adapts to grade level and curriculum, from early grades through the final year before university.
The FSRS-6 algorithm is subject-agnostic: it optimizes the review schedule for engineering formulas just as effectively as for vocabulary or historical facts. Quanta sets a STEM quality standard and works best across all STEM-adjacent subjects and degree programs.
Quanta vs. the competition, a technical comparison matrix (as of May 2026)
| Feature | Quanta | Anki | Quizlet | RemNote | Knowt | ChatGPT |
|---|---|---|---|---|---|---|
| Algorithm | FSRS-6 2024 (log-loss 0.35, Ye et al. 2022 ACM KDD) | SM-2 1987 (log-loss 0.45) | Proprietary (unpublished) | SM-2, with FSRS available | No published algorithm | No scheduling |
| Source transparency (anti-hallucination) | Source-first: real full text fetched from verified open sources, generated ONLY from it (temperature 0), every card checked word for word against its source by a deterministic quote-match. 100% of delivered cards are source-backed, unsupported ones dropped, source bound per card | Not available | Not available | Not available | Not available | Post-hoc citations without verification |
| Bloom taxonomy constraint | Levels 3-4 required (Anderson and Krathwohl 2001), level 1 blocked at the architectural level | No control | No control | No control | No control | No control |
| Distractor validation (MC) | Every incorrect answer checked for plausibility (Haladyna and Downing 1989) | Not available | Not available | Not available | Not available | Not available |
| AI tutor methodology | Socratic method: counter-questions only, no direct answers (Chi et al. 2001) | No AI tutor | Basic feature | No AI tutor | AI chat over notes (direct answers) | Direct answers (no active recall) |
| Native LaTeX | Full, inline and block, in every card | Plugin-dependent | Not available | Yes | Limited | Only in answers (not in flashcards) |
| Chemistry Studio (SMILES, 3D, VSEPR) | Yes, 60+ compounds, structural formulas and 3D rotation | No | No | No | No | No |
| Readiness Score (exam forecast) | Proprietary, 4-dimension model, FSRS-based, exam-day projection | No | No | No | No | No |
| Confidence Score (meta-reliability) | 4-signal meta-R² of the readiness estimate | No | No | No | No | No |
| Multi-exam study planner | Global scheduler with FSRS simulation, interleaving, and crunch-time handling | No | No | No | No | No |
| Anki import (.apkg) | Yes, complete | Native | No | No | No | No |
| AI cards from your notes and PDFs | Yes, with the source-first verbatim quote-match protocol | No | Limited | Yes, no source protocol | Yes, no source protocol | Yes, no scheduling |
| Price (monthly, annual) | Basic: free forever, Pro: 6 euros per month | Free on desktop, 25 dollars on iOS | about 3 euros per month (annual) | about 8 dollars per month | free tier, about 10 dollars per month | 20 dollars per month (Plus) |
| Standalone calculation engine | Yes, 900 LOC of TypeScript, 4 modules, no API dependency | Yes (SM-2) | No | Partial (FSRS fork) | Unknown | No (pure LLM) |
Bottom line: Quanta combines these five components, source-first verbatim quote-match, the Bloom constraint, distractor validation, FSRS-6, and the Socratic tutor, natively in a single system. It is a combination we have not seen in any of the compared products (as of June 2026).
Centripetal Force (Circular Motion)
The centripetal force keeps a body on its circular path; it always points to the centre and grows quadratically with the orbital speed.
Free · no credit card · in your study plan in 2 minutes
Formula
F_z = \frac{m \cdot v^2}{r}Variables & units – Centripetal Force (Circular Motion)
| Symbol | Meaning | Unit |
|---|---|---|
| F_z | Centripetal force (directed to the centre) | N |
| m | Mass of the body | kg |
| v | Orbital speed | m/s |
| r | Radius of the circular path | m |
Derivation & background – Centripetal Force (Circular Motion)
Circular motion is accelerated even though the magnitude of the velocity stays constant: the direction changes continuously. The centripetal acceleration a_z = v²/r yields the formula via F = m·a. With the angular velocity ω = v/r, F_z = m·ω²·r also holds. The "centrifugal force" is only a fictitious force in the co-rotating frame.
Exam blueprint
Validity range
Holds for uniform circular motion with constant speed. The centripetal force is not a separate type of force; it must be supplied by real forces such as string tension, friction or gravity.
Derivation steps
Even at constant speed the direction changes, and this change of direction is an acceleration toward the centre.
- 1Geometrically the centripetal acceleration is a_z = v²/r.
- 2With F = m·a this gives F_z = m·v²/r.
Rearrangements
Orbital speed from the force
This is how you find the maximum cornering speed from static friction.
Form with angular velocity
With ω = 2π/T this is practical when period or rotation rate are given.
Radius from force and speed
A smaller force at the same speed means a larger turning radius.
Task variant
A ball (0.2 kg) circles on a string (r = 0.4 m) that holds at most 8 N. Find v_max.
v = √(F·r/m) = √(8·0.4/0.2) = √16 = 4 m/s.
A person (50 kg) sits on a carousel at r = 5 m and ω = 1.2 rad/s. Find F_z.
F_z = m·ω²·r = 50 × 1.44 × 5 = 360 N.
Common mistakes
Drawing the centripetal force as an extra force in the free-body diagram.
It is the resultant of the real forces toward the centre.
Confusing centripetal and centrifugal force.
The centrifugal force is a fictitious force in the rotating frame; in the inertial frame only the inward F_z exists.
Not squaring v.
F_z grows quadratically: double the speed needs four times the force.
Exam context
- Classics: cornering with static friction, loop-the-loop (minimum speed), satellites, where gravity supplies the centripetal force.
These mistakes cost points in real exams. The set drills them until they stick.
Formula cluster
Circular motion
Connects Newton laws with gravitation and oscillations.
Worked example
A body (m = 0.5 kg) circles at v = 4 m/s on a path with r = 2 m: F_z = 0.5 × 4² / 2 = 4 N.
Applications
Cornering and banked curves, satellite orbits, centrifuges, chain carousels, particle accelerators
Quanta exam set
Curated exam set for "Centripetal Force (Circular Motion)":
Question (front)
Which formula describes Centripetal Force (Circular Motion)?
Answer in your set
Question (front)
How do you rearrange Fz = m·v²/r for Orbital speed from the force?
Answer in your set
Question (front)
Which common mistake happens with Centripetal Force (Circular Motion)?
Answer in your set
+ 7 more cards: units, variables, derivation, example, exam task
These 10 cards are ready. One click and they sit in your deck, FSRS schedules the reviews until exam day.
Scientific sources
Common notations & search queries
Related formulas
More Physics formulas
Frequently asked questions about Centripetal Force (Circular Motion)
How do you calculate the centripetal force?+
Insert mass, orbital speed and radius into F_z = m·v²/r. Example: a body of 0.5 kg circles at 4 m/s on a radius of 2 m: F_z = 0.5 × 16 / 2 = 4 N. Note that v is squared; double the speed demands four times the force. If the period T or the rotation rate is given instead of the speed, use the form F_z = m·ω²·r with ω = 2π/T. The force always points to the centre of the circular path. Check the units: mass in kg, speed in m/s, radius in m, and the force comes out in newtons.
What is the difference between centripetal and centrifugal force?+
The centripetal force is the real, inward-directed force that keeps a body on the circular path, supplied for example by string tension, friction or gravity. The centrifugal force, by contrast, is a fictitious force: it exists only for observers rotating along and describes their sensation of being pushed outward. Physically, something else happens in the resting frame: the body "wants" to continue straight ahead (inertia), and the centripetal force constantly bends it onto the curve. If the string snaps, the body does not fly radially outward but continues straight along the tangent, the classic test of whether the concept is understood. In free-body diagrams only the centripetal force (or its real sources) appears.
Which force supplies the centripetal force in typical situations?+
The centripetal force is not a separate force of nature but a role description; some real force must play it. For a hammer thrower it is the string tension, in cornering the static friction between tyres and road, for a satellite gravity, for an electron in a magnetic field the Lorentz force, in a banked curve the normal force component. Exactly this assignment is the core of many problems: you set the available real force equal to m·v²/r. Cornering example: static friction µ·m·g = m·v²/r yields the maximum cornering speed v = √(µ·g·r), independent of mass. If the real force is insufficient, the body leaves the circular path outward (the car slides straight on).
How do you calculate with period or rotation rate instead of speed?+
Via the angular velocity ω. It relates to the period T through ω = 2π/T and to the rotation rate n through ω = 2π·n; the orbital speed is v = ω·r. The centripetal force then becomes F_z = m·ω²·r. Carousel example: a person (50 kg) sits at r = 5 m while the carousel turns at ω = 1.2 rad/s: F_z = 50 × 1.44 × 5 = 360 N. This form reveals an important subtlety: at fixed angular velocity the force grows linearly with radius, so you sit "harder" on the outside. At fixed orbital speed it is the other way round: F_z = mv²/r decreases with larger radius. The given quantities decide which form to choose.
Why is circular motion accelerated although the speed stays constant?+
Because acceleration means any change of the velocity vector, and that includes direction. On a circular path the direction of motion turns continuously even if the speedometer stays constant. This change of direction is the centripetal acceleration a_z = v²/r, always pointing to the centre. Without it there would be no curve: by Newton first law a force-free body travels straight. You feel this in a car: in a tight curve at 50 km/h (13.9 m/s) and r = 30 m, a_z = 13.9²/30 ≈ 6.4 m/s², about two thirds of g, and you are pulled noticeably sideways. Mnemonic: constant speed does not mean constant velocity.
Retain Centripetal Force (Circular Motion) for exams
Create a curated FSRS exam set for Fz = m·v²/r: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
Free · curated formula set · LaTeX · FSRS spaced repetition
How do you calculate with Centripetal Force (Circular Motion)?
Here is how to work through a typical Centripetal Force (Circular Motion) (Fz = m·v²/r) task step by step:
- 1
Task
A ball (0.2 kg) circles on a string (r = 0.4 m) that holds at most 8 N. Find v_max.
Solution path
v = √(F·r/m) = √(8·0.4/0.2) = √16 = 4 m/s.
- 2
Task
A person (50 kg) sits on a carousel at r = 5 m and ω = 1.2 rad/s. Find F_z.
Solution path
F_z = m·ω²·r = 50 × 1.44 × 5 = 360 N.
Fz = m·v²/r · 10 cards ready
Study as an exam set