Physical quantities — fundamental and derived: Visual walkthrough

1.1.1 · D2 · Physics › Measurement, Vectors & Kinematics › Physical quantities — fundamental and derived

Hum sirf teen fundamental quantities assume karte hain: length, mass, aur time. Baaki sab build kiya jaata hai. Toh chalte hain build karne.

Step 1 — Teen tools jo hum use kar sakte hain

KYA. Hum bilkul teen measuring instruments rakhte hain aur kuch nahi: ek ruler jo length measure karta hai, ek scale jo mass measure karta hai, aur ek stopwatch jo time measure karta hai.

KYU. Tum ek unit derive nahi kar sakte jab tak pehle yeh agree na karo ki kya derived nahi hai. Yeh teeno fundamental hain: har ek ko directly ek standard ke against measure kiya jaata hai, koi bhi doosre ko use karke define nahi hota. Force is table par nahi hai — yahi poori baat hai. Hume ise construct karna hoga.

PICTURE. Neeche ke teen boxes hamare poore toolkit hain. Har ek mein ek symbol hai (woh letter jo physicists uske dimension ke liye use karte hain) aur ek SI unit.

Figure — Physical quantities — fundamental and derived

Step 2 — Speed: hamare building ka pehla act (length ÷ time)

KYA. Hum ruler aur stopwatch ko combine karte hain speed banane ke liye: time ke per unit kitni distance cover hoti hai.

KYU. Force ko acceleration chahiye, aur acceleration speed ke upar build hota hai, jo ki length aur time ke upar build hota hai. Toh hum ladder ko ek rung ek time mein chadhte hain. Hum division use karte hain kyunki "per" ka matlab hamesha divide hota hai: distance per time.

PICTURE. Ek dot distance $Δ L$ (length mein change, orange bar) travel karta hai ek time $Δ T$ (blue bar) mein. Speed ek bar dusre se divided hai.

$s^{- 1}$ kyun? $\frac{1}{s}$ ko $s^{- 1}$ likhna pure bookkeeping hai: denominator mein jo unit hai usse negative exponent milta hai. Isse hum units ko baad mein ordinary algebra ki tarah multiply aur divide kar sakte hain — woh trick jo poori derivation ko kaam karati hai.

Step 3 — Acceleration: speed khud kitni tezi se change hoti hai (speed ÷ time)

KYA. Hum dobaara time se divide karte hain acceleration banane ke liye: jis rate par speed change hoti hai.

KYU. Force motion change karke kaam karti hai — shuru karke, rokke, modhke. "Motion ka change per second" bilkul acceleration hai. Toh force acceleration se tied hogi, aur hume pehle uski units chahiye. Hum speed ko time se divide karte hain kyunki acceleration poochta hai "kitni speed per second gain hui".

PICTURE. Do speed arrows ek second apart. Green arrow woh extra speed hai jo gain hui. Acceleration woh green gain hai divided by woh time jitna laga.

Step 4 — Woh physical law jo force ko naam deta hai: $F = ma$

KYA. Hum physics ka woh ek piece introduce karte hain jo force ko define karta hai — Newton's second law: force equals mass times acceleration.

KYU. Hum force ke liye units hawa mein nahi bana sakte; ek law hume batana chahiye ki force kya hai. Law kehta hai: usi amount mein ek bhaari object ko accelerate karne ke liye, tumhe proportionally zyada force chahiye ( $\times M$ ), aur isse zyada tezi se accelerate karne ke liye bhi zyada force chahiye ( $\times a$ ). Multiplication dono "zyada mass" aur "zyada acceleration" ko capture karta hai.

PICTURE. Same push (orange arrow) ek halke aur ek bhaari block par. Bhaare block ko kam speed gain hoti hai — uska acceleration arrow chota hai. Force right side ke dono factors ka product hai.

Step 5 — Units ko algebra ki tarah multiply karo newton paane ke liye

KYA. Hum har factor ki units substitute karte hain aur unhe saath multiply karte hain.

KYU. Kyunki quantities multiply hoti hain, unki units bhi multiply hoti hain — units bilkul wahi arithmetic follow karti hain jo unke aage ke numbers follow karte hain. Yahi is poore chapter ka master principle hai.

PICTURE. Mass-unit box ( $kg$ ) acceleration-unit box ( $m s^{- 2}$ ) ke saath baitha hai; hum unhe ek combined block mein snap karte hain aur block ko ek nickname dete hain: newton.

Step 6 — Degenerate cases (kabhi skip mat karo yeh)

KYA. Hum check karte hain ki recipe extremes par kya kehti hai: zero acceleration, zero mass, aur opposite direction.

KYU. Ek derivation jis par tum bharosa karo usse apne edge cases survive karne chahiye. Agar formula $a = 0$ par nonsense deta, toh hum ise $a \neq = 0$ par bhi nahi maante.

PICTURE. Teen mini-scenarios stack kiye: ek block constant speed par drift kar raha hai ( $a = 0$ ), ek hypothetical massless object, aur ek block doosri taraf push kiya gaya (negative force).

Step 7 — Usi machine ko reuse karna: energy aur pressure ek hi nazar mein

KYA. Ek baar force build ho jaaye, baaki sab ek aur multiply ya divide hai.

KYU. Yeh dikhane ke liye ki newton ek baar ka trick nahi tha: wahi "units algebra ki tarah multiply hoti hain" engine turant joule aur pascal build karta hai.

PICTURE. Ek flow: newton $\times$ metre $\to$ joule; newton $\div$ area $\to$ pascal.

Ek-picture summary

Poora page ek image mein: teen tools se shuru karo, do baar time se divide karo acceleration tak pahunchne ke liye, mass se multiply karo (Newton's law), aur $kg m s^{- 2} = N$ padho — phir ek aur operation se joule aur pascal tak branch karo.

Recall Feynman retelling — ek 12-saal ke bachche ko batao

Mere paas sirf ek ruler, ek scale, aur ek stopwatch hai. Pehle main ruler aur stopwatch saath use karta hoon: distance divided by time mujhe speed deti hai — kuch kitna tezi se move karta hai. Phir main stopwatch dobaara speed par use karta hoon: har second mein kitni speed gain hoti hai woh acceleration hai. Ab yahan woh ek natural law hai jo mujhe chahiye — kisi bhaari cheez ko push karna, ya use zyada tezi se speed up karne ke liye push karna, dono mein zyada push chahiye, toh push = mass × acceleration. Jab main unke labels ko us hi tarah multiply karta hoon jaise main numbers multiply karta hoon, toh mujhe $kg \times m/s/s = kg m s^{- 2}$ milta hai, aur hum us pile ko "ek newton" nickname dete hain. Maine kabhi "force meter" nahi kharida — maine force teen saste tools se build ki. Aur ek baar force mil jaaye, ek aur multiply energy deta hai (joule) aur ek aur divide pressure deta hai (pascal). Mechanics poora LEGO hai, aur length-mass-time starter bricks hain.

Active recall

Recall Khud rebuild karo

Sirf $L$ , $M$ , $T$ se shuru karke, newton ki units derive karo. Har division/multiplication aur uska reason batao.
Acceleration mein $s^{- 2}$ kyun hota hai, $s^{- 1}$ kyun nahi?
$1 N$ , $1 J$ , aur $1 Pa$ ke base units kya hain?
Agar $a = 0$ ho, toh force kya hai aur uski unit kya hai?
Kya leftward force ki unit rightward force se alag hoti hai? Explain karo.

1 N

base units mein kya hai?

kg m s^{- 2}

Acceleration ka exponent

- 2

kyun hai?

humne time se do baar divide kiya (ek baar speed ke liye, ek baar acceleration ke liye)

1 J

base units mein kya hai?

kg m^{2} s^{- 2}

(force × distance)

1 Pa

base units mein kya hai?

kg m^{- 1} s^{- 2}

(force ÷ area)

a = 0

par force kya hogi?

0 N

— unit

kg m s^{- 2}

rehti hai, sirf number zero hota hai

Kya units direction carry karti hain?

Nahi — direction vector sign mein hoti hai; units sirf magnitude carry karti hain

Connections

Physical quantities — fundamental and derived — parent note: woh saat base quantities jisse yeh page draw karta hai.
Newton's Second Law — woh law $F = ma$ jo Step 4 mein force ko naam deta hai.
Dimensional Analysis — units multiply/divide karne ki general algebra.
SI Units and Prefixes — m, kg, s ke peeche ke standards.
Vectors — kyun force apni direction sign mein rakhti hai, unit mein nahi.
Errors and Significant Figures — har measured $L$ , $M$ , $T$ mein uncertainty hoti hai.