Foundations — Newton's third law — action-reaction, common misconceptions

1.2.3 · D1 · Physics › Newton's Laws & Dynamics › Newton's third law — action-reaction, common misconceptions

Newton's third law ko use karne se pehle aapko use padhna aana chahiye. Parent note mein arrows, subscripts, masses, momenta aur derivatives ko aise use kiya gaya hai jaise aap unhe pehle se jaante ho. Yahan hum har ek ko bilkul zero se build karte hain, ek aisi order mein jahan har symbol use hone se pehle earn kiya jaata hai.

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1. "Object" ya "body" kya hota hai?

Picture hi poori baat hai: jis moment hum choose karte hain ki body kya hai, hum uske around ek imaginary bubble draw karte hain. Bubble ke andar jo kuch bhi hai woh "the body" hai; bahar ki sab kuch "baaki universe" hai jo ise push ya pull kar sakti hai.

Yeh topic ko yeh kyun chahiye. Third law ka punchline hai "dono forces do alag bodies par act karti hain." Yeh sentence tab tak meaningless hai jab tak aap exactly point nahi kar sakte ki har force kaunse bubble mein rehti hai. Parent note mein zyaadatar misconceptions do forces ko galti se ek hi bubble mein daal dene se aate hain.

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2. Arrows: vector kya hota hai

Hum ek vector ko upar ek chhota arrow laga kar likhte hain, jaise $\vec{F}$. Bina arrow ke plain letter, $F$, sirf uski size (jise magnitude bhi kehte hain) darshata hai, kabhi direction nahi.

"Ek vector ke aage minus sign lagao" wala tool, $-\vec{F}$, ka matlab hai: same length rakho, arrow ko bilkul ulti taraf flip karo. Yeh poore page par sabse important notation hai — third law hi yeh sentence hai ${\vec{F}}_{A\to B}=-{\vec{F}}_{B\to A}$, jiska matlab hai "same length, flipped direction."

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3. Force: push ya pull

Force hamesha ek body ka doosri body par act karna hota hai. Aisi koi force nahi hoti jo bas kisi ki bhi nahi ho. Isliye hume labels ki zaroorat hai.

Jab tak automatic na ho jaye, har baar zor se padho:

• ${\vec{F}}_{A\to B}$ ::: "force from A on B."
• ${\vec{F}}_{B\to A}$ ::: "force from B on A."

Third law kehti hai yeh dono — labels swap ke saath — equal-and-opposite hain. $A\leftrightarrow B$ swap karna literally mnemonic ke pehle "S" hai.

Yeh topic ko yeh kyun chahiye. Parent ke "true pair" checklist ke rules 4 aur 5 poori tarah in subscripts ke baare mein hain. $A\to B$ notation ke bina aap yeh bhi state nahi kar sakte ki do forces genuine pair hain ya nahi.

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4. Force ke types (kyun "same type" matter karta hai)

Parent ka rule 3 kehta hai ki ek true pair mein same type ki force honi chahiye. Toh hume common types ke naam jaanne chahiye:

Symbol	Plain meaning	Picture
gravity ${\vec{F}}_{E\to b}$	Earth ka ek body ko neeche ki taraf kheenchna	arrow seedha neeche Earth ke centre ki taraf
normal $\vec{N}$	ek surface ka baahir ki taraf push karna, apne aap se perpendicular	arrow 90° par table/floor se bahar
friction $\vec{f}$	ek surface ka apne saath drag karna, sliding ko oppose karte hue	arrow surface ke saath flat

Inhe aap Normal Force and Friction mein detail mein dekhoge. Abhi ke liye sirf ek cheez matter karti hai: normal aur gravity alag types hain, isliye yeh kabhi ek doosre ke partner nahi ho sakte — yeh parent ke teesre misconception ko ek hi line mein khatam kar deta hai.

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5. Mass $m$: dhakka dena kitna mushkil hai

Picture yeh hai: ek bowling ball aur beach ball same size ke ho sakte hain, lekin bowling ball ko motion mein laana bahut mushkil hota hai. Yeh "motion mein laana mushkil" hi mass hai.

Yeh topic ko yeh kyun chahiye. Parent ka sabse bada "aha" moment — truck aur mosquito ko equal forces lagti hain lekin unke outcomes bilkul alag hote hain — sirf aur sirf mass ke baare mein hai. Same force $F$, lekin $a=F/m$: tiny-mass mosquito ko monster acceleration milti hai.

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6. Velocity $\vec{v}$ aur momentum $\vec{p}$

Kyunki $\vec{p}$ mein mass factor hota hai, ek halka body aur ek bhaari body bilkul alag speeds par same momentum rakh sakti hain — yahi wajah hai ki parent ke do ice skaters (60 kg vs. 40 kg) ek momentum-swap share karte hue alag alag speeds se alag hote hain. Aap ise Conservation of Momentum mein bahut zyaada use karoge.

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7. Rate-of-change symbol $\frac{d}{dt}$

Parent ki derivation mein $\frac{d\vec{P}}{dt}$ likha hai. Yeh daraaune lagta hai; hai nahi.

Do facts hi kaafi hain:

1. Ek constant ka rate of change zero hota hai: agar $\vec{P}$ kabhi nahi badlta, toh $\frac{d\vec{P}}{dt}=0$.
2. Momentum ka rate of change = force. Yahi Newton ka *second* law hai apni sachchi form mein: $\frac{d\vec{p}}{dt}=\vec{F}$. Force kuch nahi balki momentum kitni tezi se badalta hai.

Ab parent ki poori derivation plain words mein padhi ja sakti hai: ek isolated pair ka total motion kabhi nahi badlta (rate = 0); har body ke motion ka rate of change us par lagi force hai; toh dono forces ka sum zero hona chahiye — yaani woh equal and opposite hain. Yahi third law hai, momentum se born.

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8. Free-body diagram (workhorse tool)

Woh golden rule jo parent ke #1 misconception ("action aur reaction cancel hoti hain") ko khatam karta hai: ek 3rd-law pair kabhi same FBD mein nahi aata, kyunki dono forces do alag bodies par act karti hain, jinke do alag diagrams bante hain. Forces sirf ek hi FBD ke andar cancel ho sakti hain. Aap ise Free Body Diagrams mein practice karoge.

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Foundations topic ko kaise feed karte hain

Upar har arrow ka matlab hai "jab tak aap us box ko nahi samjhoge jahan se arrow aa raha hai, tab tak aap us box ko nahi samjhoge jahan arrow ja raha hai." Poora page left-hand boxes bharne ke liye exist karta hai.

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Equipment checklist

Right side cover karo aur khud ko test karo. Agar koi bhi jawab fuzzy lage, parent note chhune se pehle woh section dobara padho.

• $\vec{F}$ par chhota arrow kya darshata hai, aur plain $F$ kya darshata hai? ::: $\vec{F}$ mein size aur direction (ek arrow) dono hain; plain $F$ sirf size (magnitude) hai.
• ${\vec{F}}_{A\to B}$ mein, kaunsi body actually force feel karti hai? ::: Body $B$ — subscript mein arrow us taraf point karta hai jo push ho raha hai.
• $-\vec{F}$ mein minus sign kya karta hai? ::: Same length rakhta hai, direction ko exactly ulta flip karta hai.
• Mass kya hai, ek phrase mein? ::: Body kitni ziddi hai — speed up ya slow down hone ki resistance.
• Momentum ko formula ki tarah likho aur batao yeh kya picture karta hai. ::: $\vec{p}=m\vec{v}$; body ki "quantity of motion" / unstoppability.
• $\frac{d\vec{P}}{dt}=0$ plain words mein kya kehta hai? ::: Total momentum time mein nahi badal raha — yeh constant hai.
• Kaunsa law kehta hai $\frac{d\vec{p}}{dt}=\vec{F}$? ::: Newton's second law — force momentum ke rate of change hai.
• 3rd-law pair kabhi cancel kyun nahi ho sakti? ::: Dono forces do alag bodies par act karti hain, isliye woh do alag free-body diagrams mein rehti hain; cancellation ke liye forces same body par chahiye.
• Normal force aur gravity same type ki force hain? ::: Nahi — ek surface ka contact push hai jo perpendicular hoti hai, doosri Earth ka pull hai; alag types kabhi partners nahi ho sakte.
• Truck aur mosquito par same force — outcomes alag kyun? ::: $a=F/m$; mosquito ki tiny mass bahut badi acceleration deti hai.

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Connections

• Newton's Second Law — $\vec{F}=m\vec{a}$ aur momentum form $d\vec{p}/dt=\vec{F}$ supply karta hai jo yahan use hoti hai.
• Conservation of Momentum — yeh fact "$d\vec{P}/dt=0$" jis par poori derivation tikhi hai.
• Free Body Diagrams — woh tool jo har force ko sahi bubble mein rakhta hai.
• Normal Force and Friction — woh force types jinki distinctness "normal = reaction to gravity" myth ko khatam karti hai.
• Rocket Propulsion & Variable Mass — jahan momentum aur third law combine hote hain.
• Center of Mass Motion — jahan "total momentum of a system" ka natural home hai.