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

1.2.3 · Physics › Newton's Laws & Dynamics

WHAT hai third law?

Aakhri phrase hi sab kuch hai: pair alag bodies par kaam karta hai. Yahi log bhool jaate hain.

WHY sach hai yeh? (Conservation of momentum se derivation)

Newton ne asliyat mein third law ko postulate kiya tha, lekin hum dikha sakte hain ki yeh ek gehri baat ke barabar hai: isolated system ka momentum conserve hota hai. Chaliye ise scratch se derive karte hain.

Do particles $A$ aur $B$ lo jo sirf ek-doosre se interact karte hain (isolated system). Total momentum: $P = p_{A} + p_{B} = m_{A} v_{A} + m_{B} v_{B}$

Yahan se kyun shuru karein? Kyunki "isolated" ka matlab hai koi bhi external cheez kaam nahi kar rahi, toh experimentally hum dekhte hain ki $P$ time ke saath constant rehta hai.

Time ke saath differentiate karo: $\frac{d P}{d t} = \frac{d p _{A}}{d t} + \frac{d p _{B}}{d t} = 0$

Yeh step kyun? Ek constant vector ka time-derivative zero hota hai.

Newton ki second law se, $\frac{d p _{A}}{d t} = F_{on A} = F_{B \to A}$ ( $A$ par sirf $B$ ki force kaam kar rahi hai). Usi tarah $B$ ke liye: $F_{B \to A} + F_{A \to B} = 0 ⟹ F_{A \to B} = - F_{B \to A}$

Yeh kyun matter karta hai: third law arbitrary nahi hai — yeh us baat ki guarantee hai ki momentum conserve hota hai. Agar forces equal-opposite pairs mein nahi aate, toh ek isolated system spontaneously apna momentum change kar sakta tha, aur tum ek aisi machine bana sakte the jo bina kisi exhaust ke khud aage dhakelte — (impossible hai yeh).

HOW sahi tarike se use karna hai ise

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

Worked examples

Common misconceptions (Steel-man + fix)

Recall Feynman: 12-saal ke bachche ko explain karo

Jab tum wall ko push karte ho, wall tumhare haath ko utni hi zor se wapas push karti hai — isliye tumhara haath darta hai, wall nahi! Tum kisi cheez ko push nahi kar sakte bina uske tumhe push kiye. Jab tum chalte ho, tum apne paon se zameen ko peeche push karte ho, aur zameen tumhe aage push karti hai — woh aage ki push hi tumhe chalati hai. Rocket bhi usi tarah kaam karta hai: woh gas ko neeche fenkta hai, gas rocket ko upar fenkta hai. Hamesha ek "tu mujhe push karo, main tujhe push karun" wala deal hota hai, aur dono pushes hamesha bilkul same strength ki hoti hain — lekin halki cheez zyada tezi se speed up hoti hai kyunki use dhakkelna aasaan hota hai.

Active-recall flashcards

Newton's third law ko equation ke roop mein batao.

F_{A \to B} = - F_{B \to A}

(equal magnitude, opposite direction, do alag bodies par).

Ek 3rd-law pair ki dono forces hamesha kis par kaam karti hain…

do alag objects par (kabhi bhi same par nahi).

Action–reaction forces cancel kyun nahi hoti aur sab kuch rok deti?

Yeh alag bodies par kaam karti hain, toh alag free-body diagrams mein aati hain; cancellation ke liye forces ek hi body par chahiye.

Ek truck ek machhar se takrata hai. Kaun zyada force feel karta hai?

Koi nahi — forces magnitude mein bilkul equal hain.

Phir machhar kyun tabah ho jaata hai aur truck nahi?

a = F / m

; machhar ka chhota mass same force ke liye ek bada acceleration deta hai.

Kya book par normal force uske weight ki reaction hai?

Nahi — dono book par kaam karti hain aur alag force types hain. Weight ka partner hai "book pulls Earth up"; normal ka partner hai "book pushes table down".

Third law kaunse gehre conservation law ke barabar hai?

Conservation of momentum of an isolated system.

Momentum conservation se third law derive karo (ek line mein).

d P / d t = 0 \Rightarrow F_{B \to A} + F_{A \to B} = 0

Do skaters (60 kg, 40 kg) push off karte hain. Unki speeds ka ratio kya hai?

∣ v_{40} ∣/∣ v_{60} ∣ = 60/40 = 1.5

; halka wala zyada tez hoga.

Kya action aur reaction mein time delay hoti hai?

Nahi — yeh simultaneous hote hain.

Rocket vacuum mein kaise accelerate karta hai jab kuch push karne ko nahi hota?

Yeh ejected gas ko peeche push karta hai; gas ki reaction rocket ko aage push karti hai (partner exhaust hai, air nahi).

Connections

Newton's Second Law — $a = F / m$ deta hai, yeh explain karta hai ki equal forces unequal accelerations kyun cause karti hain.
Conservation of Momentum — third law iska microscopic origin hai.
Free Body Diagrams — woh tool jo same-body forces ko action-reaction pairs se alag karta hai.
Normal Force and Friction — misidentified pairs ki common jagahein.
Rocket Propulsion & Variable Mass — action-reaction ka direct application.
Center of Mass Motion — internal 3rd-law forces kabhi bhi COM ko move nahi karti.