Foundations — Newton's first law — inertia, operational definition of force

1.2.1 · D1 · Physics › Newton's Laws & Dynamics › Newton's first law — inertia, operational definition of forc

Yeh page kuch bhi assume nahi karta. Parent note mein jo bhi letter, arrow, aur squiggle use hua hai, woh sab yahan ground up se build kiya gaya hai, uss order mein jisme har ek cheez pichli par tikhi ho.

1. Position — "koi cheez kahan hai"

Motion se pehle, hume location chahiye. Ek starting dot chuno (isko origin kaho) aur do number-lines us par cross karte hue rakh do: ek right jaati hai (use $x$ kaho), ek upar jaati hai (use $y$ kaho). Koi bhi point tab "itne steps right, itne steps upar" hota hai.

Figure s01 dekho: black corner origin hai, do black arrows $x$ aur $y$ axes hain, aur red dot body hai. Dashed black lines "measuring tapes" hain jo dot ko $x=3.5$ tak neeche aur $y=2.4$ tak side mein le jaati hain — woh do numbers hi us body ki position hain.

2. Arrow — vector kya hota hai

Physics mein bahut si quantities ko ek saath do baatein chahiye: kitna aur kis direction mein. "5 metres north" alag hai "5 metres east" se. Hum aise quantity ko ek arrow ki tarah draw karte hain: uski length "kitna" hai, aur woh jis taraf point karta hai woh "kis direction mein" hai.

Woh chota arrow-hat $\stackrel{⃗}{}$ parent note ka tarika hai yeh quietly kehne ka ki "is cheez ki ek direction hai — mat bhoolo." Jab bhi $\vec{F}$ ya $\vec{v}$ dekho, "arrow" padhna.

3. Arrows ko add aur subtract karna

Change ki baat karne se pehle, hume arrows combine karne aana chahiye. Yeh arrow-arithmetic ka woh ek piece hai jis par poora topic depend karta hai.

Figure s02 dekho: do arrows add karne ke liye, doosre ka tail pehle ki tip par rakho (tip-to-tail); arrow jo bilkul shuruat se bilkul end tak jaata hai woh sum hai. ${\vec{v}}_i$ ko ${\vec{v}}_f$ se subtract karne ke liye (likha jaata hai ${\vec{v}}_f-{\vec{v}}_i$), ${\vec{v}}_i$ ko reverse karo (use $180°$ flip karo) aur woh add karo — ${\vec{v}}_i$ ki tip se ${\vec{v}}_f$ ki tip tak ka red arrow difference hai.

4. Time — woh coordinate jo cheezein change hone deta hai

Position akela ek frozen snapshot hai. Motion ke liye ek doosri cheez chahiye jiske against plot karein: time.

5. Velocity — woh arrow jis par poora law hai

Ab position + time + arrow combine karo. Velocity woh arrow hai jo batata hai ki position-dot time ke saath kaise badal raha hai: kitna tez, aur kis direction mein.

Figure s03 dekho: black dot body hai abhi; red arrow $\vec{v}$ us taraf point karta hai jahan woh ja rahi hai, aur uski length batati hai kitna tez. Aage faint dot dikhata hai ki thodi si time $t$ baad woh kahan hogi.

Units: velocity metres per second mein measure hoti hai, likha jaata hai $\text{m/s}$ — "time $t$ ke har second mein kitne metres position gain hoti hai."

6. "Change" aur symbol $\Delta$

Law motion mein change ke baare mein hai. Hume ek symbol chahiye "koi cheez kitni badli" ke liye. Woh symbol hai Greek capital delta, $\Delta$.

Chota time-interval $\Delta t$ — final clock-reading minus start clock-reading — yeh measure karta hai ki ek change kitne time mein hua. Ek quick-yank trick mein (jaise dishes ke neeche se cloth kheenchna), $\Delta t$ bahut chota hota hai, isliye chahe real friction force ho, woh itni briefly act karti hai ki velocity zyada nahi badal pati.

7. Acceleration — force ki symptom

Agar velocity motion-arrow hai, toh acceleration hai "woh arrow kitna tez badal raha hai." Yeh khud bhi ek arrow hai.

Arrow teen tarike se badal sakta hai, toh teen tarike se accelerate ho sakta hai:

Teeno acceleration count karti hain — teesri wali woh sneaky case hai jiske baare mein parent note baar baar warn karta hai.

8. Force — cause, likha jaata hai $\vec{F}$

Ab parent note ka star. Force ek push ya pull hai. Tum use directly kabhi nahi dekhte; acceleration se infer karte ho.

Figure s04 dekho: chaar black force-arrows body ko left, right, upar, aur neeche push kar rahe hain. Kyunki thrust drag cancel karta hai aur lift weight cancel karta hai, woh sab zero vector tak add ho jaate hain — red dot ${\vec{F}}_{\text{net}}=\vec{0}$ mark karta hai.

Poore topic ka core statement, ab symbol-by-symbol fully readable: ${\vec{F}}_{\text{net}}=\vec{0}⟺\vec{v}=\text{constant}$

Zor se padho: "Net push-arrow zero vector hai if and only if motion-arrow kabhi nahi badlta." Double arrow $⟺$ matlab dono directions true hain: no net force guarantee karta hai constant velocity, aur constant velocity guarantee karta hai no net force.

9. Mass — stubbornness measure karne wala number

10. Frame of reference — hum kahan se dekh rahe hain

Aakhri hidden idea. Position aur velocity ki har measurement kahan se ki jaati hai — zameen par khade hokar, ya bus mein baith ke. Woh viewpoint ek frame of reference hai.

Prerequisite map

Equipment checklist

Khud test karo — right side cover karo aur reveal karne se pehle har ek ka jawab do.

Connections

• Newton's first law — inertia, operational definition of force — woh parent jiske liye yeh page tumhe tayaar karta hai.
• Newton's second law — F=ma — force-arrow ko mass aur acceleration use karke ek number mein convert karta hai.
• Newton's third law — action-reaction — force-arrows hamesha pairs mein aate hain.
• Inertial vs non-inertial frames — jahan first law rehne ki permission hai.
• Friction — woh hidden force-arrow jisne Aristotle ko ullu banaya.
• Uniform circular motion — turning-arrow case poori tarah se.
• Pseudo-forces — non-inertial frames mein invented arrows.
• Mass vs weight — stubbornness number vs gravity arrow.