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The guide defines key gear terminology, explains drive and driven gears, idler gears, and compound gears, and shows how tooth counts determine rotational direction and ratio. It includes worked examples using STELR solar car components, then prompts students to compute ratios for different gear trains and design their own gear diagrams to compare speed versus torque outcomes.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mathematics-of-gears-investigation-into-how-gears-work-calculating-gear-ratios/167362/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mathematics-of-gears-investigation-into-how-gears-work-calculating-gear-ratios/167362.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-20","2026-08-31",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you calculate a simple gear ratio using tooth counts?","Question",{"text":112,"@type":113},"Divide the number of teeth on the driven gear by the number of teeth on the drive gear. The result tells how many turns the drive gear makes for one turn of the driven gear.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What role do idler gears play in a gear train?",{"text":117,"@type":113},"Idler gears change direction of rotation or extend the distance between drive and driven gears, but they do not contribute to the gear ratio regardless of their size.",{"name":119,"@type":110,"acceptedAnswer":120},"How is the gear ratio determined for a compound gear train?",{"text":121,"@type":113},"Multiply the gear ratios of each stage in the compound gear train. The final ratio comes from combining stage ratios, based on tooth counts of the outside and inside compound rings and the driven gear.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},167362,1788212095,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":31},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","MATHEMATICS OF GEARS  \nINVESTIGATION INTO HOW GEARS WORK  \nINTRODUCTION  \nYou may know that gears on a bike make it easier to pedal uphill or faster to go along the flat, but how do they actually make a difference?  \nIn this investigation we look at how to calculate gear ratios and what differences they make to driving a car (or riding a bike)  \nEQUIPMENT  \nSTELR solar car kit  \nScrewdriver  \nINQUIRY QUESTION  \nWhat are the most efficient gear combinations to make my solar car:  \na. Go faster,  \nb. Go up a steeper hill, or  \nc. Pull with more power?  \nVOCABULARY  \nGear,  \nDrive gear,  \nDriven gear, Gear train, Idler gear, Compound gear, Crown gear, Torque  \nBACKGROUND INFORMATION  \nGears  \nGears are examples of wheel and axle machines.  \nGears have evenly spaced teeth called cogs.  \nA cog is a tooth on the rim of a wheel or gear.  \nThe cogs on gears fit into each other so that when one gear turns, it causes the other gear to turn.  \nIf two gears are connected, when one gear turns clockwise, it will cause the next gear to turn anticlockwise.  \nDrive and driven gears  \nThe drive gear, or input gear, takes the energy from the motor and transfers it to the driven gear, or output gear, to make the axle spin.  \n\n| | | |\n| --- | --- | --- |\n| Drive gear or input gear (attached to motor) . | Driven gear or output gear (attached to axle) . | Compound gear\u003Cbr>A compund gear has two (or more) gears fixed together. |\n\nExample  \nThe STELR wind turbine has two gears as shown in this photo.  \nThe top gear has 30 teeth. The bottom gear has 12 teeth.  \nIf the top gear rotates once, 30 teeth will pass through the point of contact. The bottom gear will have to rotate 2.5 times so that 30 teeth also pass through the point of contact.  \nIf the top gear rotates in a clockwise direction, the bottom gear will rotate in the anticlockwise direction.  \nIdler gears  \nA system of gears working together are known as a gear train. In a simple gear train the gears between the drive gear and driven gear are idler gears. These do not contribute to the gear ratio (no matter what their size), but change direction of rotation or extend the distance between the drive and the driven gear.  \nIn the diagram below, the arrow,  , shows the direction of rotation for the drive gear.  \nIdler gear  \nDriven  \ngear  \nDrive gear  \nFor each gear, write down the direction of rotation (clockwise or anticlockwise) .  \nDrive gear: Clockwise  \nIdler Gear:    \nDriven gear:    \nGear ratios  \nTo calculate the gear ratio, divide the number of teeth on the driven gear by the number of teeth on the drive gear. Using the gears with your solar car, or the picture above, first count the number of teeth on each gear, and then calculate the gear ratio.  \nGear ratio = \\#\\#teteetehthoonndrivedrivneggeeaarr  \n32  \n= ~~ ~~  \n8  \n4  \n= ~~ ~~  \n1  \nOr 4:1  \nThe drive gear turns 4 times to make the driven gear turn once.  \nFor another explanation on how to calculate gear ratios go to  \n[http://www.wikihow.com/Determine-Gear-Ratio](http://www.wikihow.com/Determine-Gear-Ratio)  \nCompound gears  \nIn a gear train with compound gears, like in the solar car, the gear ratio does change. The benefits of compound gear trains are you can change the speed of the gears and as the gears overlap, the gear trains takes up less space.  \nDrive  \ngear   \nCompound gear  \n Driven gear  \nTo calculate the gear ratio of a compound gear, multiply the gear ratios of each stage of the gear train.  \nStage 1 drive gear (purple in the photo) and outer ring of the compound gear (yellow)  \nGear ratio = \\#~~ ~~teeth\\#on~~ ~~outteethsoidnedcompounrive~~ ~~geard~~ ~~gear  \n=  \n34  \n8  \nStage 2 inner ring of compound gear (yellow) and driven gear (blue) Gear ratio = \\#~~ ~~tee\\#~~ ~~teeth~~ ~~ontih~~ ~~onnsidderivencompgoearund~~ ~~gear  \n36  \n12  \nThe final ratio is found by multiplying the two stage ratios together:  \n\\# teeth on outside compound gear \\# teeth on driven gear Final ratio = ~~ ~~ × ~~ ~~  \n\\# teeth on drive gear \\# t","cbCaioRezUEbxUId","https://ap.wps.com/l/cbCaioRezUEbxUId","pdf",2635185,"English","# Introduction\n## Equipment\n## Inquiry question\n## Vocabulary\n## Background information\n# Drive and driven gears\n## Idler gears and gear trains\n## Gear ratios\n# Compound gears\n## Calculating compound gear ratios\n# Calculate gear ratios\n## Simple meshed gear\n## Simple gear train with idler gear\n## Compound gear train\n# Create your own gear train\n## Speed vs torque observations\n# The STELR solar car gearbox","[{\"question\":\"How do you calculate a simple gear ratio using tooth counts?\",\"answer\":\"Divide the number of teeth on the driven gear by the number of teeth on the drive gear. The result tells how many turns the drive gear makes for one turn of the driven gear.\"},{\"question\":\"What role do idler gears play in a gear train?\",\"answer\":\"Idler gears change direction of rotation or extend the distance between drive and driven gears, but they do not contribute to the gear ratio regardless of their size.\"},{\"question\":\"How is the gear ratio determined for a compound gear train?\",\"answer\":\"Multiply the gear ratios of each stage in the compound gear train. The final ratio comes from combining stage ratios, based on tooth counts of the outside and inside compound rings and the driven gear.\"}]","Mathematics of Gears - Investigation Into How Gears Work - Calculating Gear Ratios | PDF"]