Yeh page kuch bhi assume nahi karta. Agar tumne kabhi kisi arrow par letter, koi Greek letter, ya upar dot waala fraction nahi dekha, toh yahan se shuru karo. Hum har symbol ko ek picture se banate hain, phir dikhate hain ki topic us symbol ke bina kaam kyun nahi kar sakta. Teen words "push" (force), "how much stuff" (mass), aur "change of motion" (acceleration) ko §1, §5 aur §6 mein theek se define kiya gaya hai, pehle koi bhi equation use karne se.
Ek rocket ko yeh kyun chahiye? Kyunki "engine 500 kilonewtons se push karta hai" — yeh tab tak bekar hai jab tak tum yeh nahi batate ki kidhar. Aage push karo toh chadhte ho; sideways push karo toh tumble karte ho. Direction aadhi kahani hai, isliye yahan har force aur motion ek vector hai.
Figure s01 — ek vector ek arrow hai: uski length size hai, jis taraf point kare woh direction hai.
Picture dekho: tilted force exactly reproduce hoti hai apne "along" part aur "across" part se. Kuch bhi kho nahi jaata — hum same push ko sirf do aasaan numbers se describe karte hain.
Figure s02 — tirchi blue push apne orange "along-axis" part aur green "across-axis" part ke barabar hai; dono components milke original arrow bana dete hain.
Topic ko iska kyun zaroorat hai: hawa ki single push awkward hoti hai. Isko "rocket ke body ke saath-saath" aur "rocket ke body ke aad mein" split karo, aur ekdam pata chal jaata hai ki airframe ko kya withstand karna padega. Yahi exactly axial aur normal force hain — body axes mein hawa ki push ke do components.
Hum measure karte hain ki koi arrow kitna teda hai ek angle se. Angle ko har component ki length mein convert karne ke liye, humein ek right triangle ke do ratios chahiye.
Figure s03 — sine aur cosine seedha right triangle se padte hain: cosine orange side ke saath pair karta hai jo angle ko touch karta hai ("along" part), sine green side ke saath jo uske saamne hai ("across" part).
Parent page teen alag directions use karta hai. Inhe confuse karna number-one trap hai, isliye hum teeno ko ek saath picture karte hain.
Figure s04 — teen directions aur do angles: green γ horizontal se velocity tak upar measure hota hai; red α velocity se body axis tak (nose flight path ke upar). Jaise draw kiya gaya hai dono positive hain.
Topic ko dono kyun chahiye: α decide karta hai ki hawa apni push kaise split karti hai (hawa mein tilt nahi, toh sideways "lift" nahi). γ decide karta hai ki gravity kitni chadhna rok rahi hai versus path curve kar rahi hai. Yeh alag-alag cheezein measure karne wale alag-alag angles hain — inhe kabhi mix mat karo.
Ek rocket ko chadhte hue socho: agar arrow v time ke saath lamba hota jaaye, toh yeh path ke saath-saath acceleration hai (speeding up). Agar v sirf rotate kare, toh yeh path ke aad mein acceleration hai (turning). Parent page Newton's law ko exactly in dono mein split karta hai — ek magnitude equation aur ek turning equation — kyunki acceleration ke yeh do chehere hain.
Ab jab force (§1), mass (neeche) aur acceleration (§5) har ek ke paas plain-words meaning aur picture hai, hum finally woh law likh sakte hain jo inhe saath bandhta hai.
Yahan ==m hai mass==: rocket mein kitna "stuff" hai, kilograms mein — yeh measure hai ki usse accelerate karna kitna mushkil hai. Yeh single equation poore topic ka engine hai; baaki sab kuch sirf yeh nikalna hai ki F mein har force kya hai.
Neeche ka map upar se neeche padhta hai: har box is page ka ek foundation hai, aur arrows dikhate hain koi idea kya feed karta hai. Koi bhi path trace karo aur build order dikh jaayega — vectors aur angles component split ko feed karte hain (axial/normal dete hain); mass aur rate-of-change dot variable-mass idea ko feed karte hain (thrust equation deta hai); aur yeh sab, Newton's law aur weight ke saath, full equation of motion mein jaate hain, jo parent topic hai.
