[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-144167-en":3,"doc-seo-144167-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},144167,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",6,"Technology","Gears - A complete study guidebook - Notes, formulas, and 20 leveled practice questions","Gears is a complete study guidebook that builds understanding from copybook notes and extends them into deeper gear physics. It presents key vocabulary, the fundamental gear law using RPM and tooth counts, direction and connection rules, gear ratio calculation, and torque–speed trade-offs via power conservation. It also explains pitch circle reasoning, compound gear trains, gear types, efficiency losses, and idler gears, then reinforces learning with 20 leveled practice questions and explanations.","Gears  \nA complete study guidebook  \nCopybook notes · extended explanations · diagrams · 20 leveled practice questions · video resources  \nTable of Contents  \nPart 1—Notes from the copybook  \nThis section reproduces exactly what's in the original notes, organized and formatted clearly.  \nKey vocabulary  \n● RPM—rotations per minute  \n● T—number of teeth  \nThe fundamental gear law  \nRPM_A · T_A = RPM_B · T_B  \nDirection rules (from the notes)  \n● Number of gears in a chain = even → different direction (first and last opposite)  \n● Number of gears in a chain = odd → same direction (first and last match)  \nGear ratio  \nG. T. = T_B / T_A = RPM_A / RPM_B  \nWorked example from the notes: T_B = 60, T_A = 20 → ratio = 3. Gear B is 3 times slower.  \nConnection rules (from the notes)  \n● On the same axle/shaft → same direction, same RPM  \n● Crossbelt → opposite direction  \nPart 2—Going deeper: what the copybook doesn't cover  \nThe notes give you the core formulas—here's the reasoning behind them, plus several important ideas that extend the topic further.  \nWhy the gear law works: the pitch circle  \nEvery gear has an imaginary circle called the pitch circle, where its teeth effectively make contact with the meshing gear. Because two meshed gears touch at this shared point, the linear (tangential) speed of both pitch circles must be identical—otherwise the teeth would jam or slip.  \nv = ω · r (linear speed = angular speed × radius)  \nSince v is the same for both gears at the mesh point, a gear with a smaller radius (fewer teeth) must have a higher angular speed (RPM) to match it. This is the physical reason behind RPM_A · T_A = RPM_B · T_B—teeth count is proportional to radius for gears of the same tooth size (module) .  \nTorque and the speed–torque trade-off  \nGears don't just change speed—they also change torque (turning force), in the opposite direction. Ignoring friction losses, power is conserved across a gear mesh:  \nTorque_A · RPM_A ≈ Torque_B · RPM_B (power in ≈ power out)  \nThis means whatever ratio you gain in speed, you lose in torque, and vice versa. A gear train that slows rotation down by a factor of 3 multiplies torque by a factor of about 3 (real systems lose a little to friction, so the real gain is slightly less than the ideal ratio) .  \nFigure—speed and torque always trade off across a gear mesh  \n● Speed-increasing gear pair (large drives small) → lower output torque, higher output speed  \n● Speed-reducing gear pair (small gear drives a big gear) → higher output torque, lower output speed  \nThis is exactly why a car uses a low gear to climb a hill (more torque, less speed) and a high gear to cruise on a highway (less torque, more speed) .  \nCompound gear trains  \nA compound gear train uses two or more gears fixed to the same shaft, so that a chain can achieve a much bigger overall ratio in a small physical space than a single mesh could. The overall ratio of a compound train is the product of each individual stage's ratio:  \nOverall ratio = (T_B/T_A) × (T_D/T_C) × ...  \nFigure—a two-stage compound gear train (B and C share a shaft)  \nThis is how real gearboxes (car transmissions, watch movements, robotics actuators) achieve large speed reductions—stacking several modest ratios in series rather than needing one impractically huge gear.  \nTypes of gears  \nThe copybook covers the math of meshing gears in general, but doesn't distinguish between the physical types. The four most common are:  \nFigure—spur, bevel, worm, and rack-and-pinion gears  \n● Spur gears—straight teeth, parallel shafts. Simple, efficient, but can be noisy at high speed.  \n● Bevel gears—cone-shaped teeth, used when shafts intersect (commonly at 90°), such as in hand drills or a car's differential.  \n● Worm gears—a screw-like \"worm\" drives a toothed wheel, giving very large speed reduction and high torque in a compact space; often self-locking (the wheel can't drive the worm backward) .  \n● Rack and pinion—a gear (pinion) meshes with a flat toothed bar (","cbCaijN3nzVMYdQE","https://ap.wps.com/l/cbCaijN3nzVMYdQE","pdf",542873,1,11,"English","en",105,"# Table of Contents\n## Part 1—Notes from the copybook\n### Key vocabulary\n### The fundamental gear law\n### Direction rules\n### Gear ratio\n### Connection rules\n## Part 2—Going deeper: what the copybook doesn't cover\n### Why the gear law works: the pitch circle\n### Torque and the speed–torque trade-off\n### Compound gear trains\n### Types of gears\n### Efficiency in real gear systems\n### Idler gears—the full picture\n## Part 3—Practice questions (easy → expert)\n## 20 questions with answers and explanations","[{\"question\":\"How does the fundamental gear law relate RPM and number of teeth?\",\"answer\":\"It states RPM_A × T_A = RPM_B × T_B, linking rotational speed to tooth counts of meshing gears.\"},{\"question\":\"What determines direction changes in a gear chain with belts?\",\"answer\":\"With an even number of gears the first and last rotate in opposite directions, while with an odd number they rotate in the same direction.\"},{\"question\":\"How do gears affect torque when they change speed?\",\"answer\":\"In ideal conditions power is conserved across a gear mesh, so increasing speed reduces output torque proportionally and vice versa.\"}]","Gears - 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