Foundations — Physical quantities — fundamental and derived

1.1.1 · D1 · Physics › Measurement, Vectors & Kinematics › Physical quantities — fundamental and derived

Ye page assume karta hai ki tumne kuch nahi dekha. Hum parent note ke har symbol ko earn karenge — $n$, $u$, $[]$, $L$, $M$, $T$, exponents jaise ${\text{s}}^{-2}$, aur units ki arithmetic — ek ek karke, har ek ko ek picture se anchor karke. Jab tum finish karo, parent ko re-read karna obvious lagega.

1. Measuring = ek standard ki copies count karna

Figure dekho. Blue bar wo cheez hai jo hum measure kar rahe hain. Choti orange tile standard hai — ek unit. Hum tile ko slide karte hain aur count karte hain: ye 5 baar fit hoti hai. Toh length hai "5 standard-tiles".

Ab hamare paas pehle do symbols hain, dono picture se earn kiye:

• $n$ = count. Picture: kitni tiles fit hain.
• $u$ = standard tile khud. Picture: akeli orange tile.

2. Smaller unit ⇒ bigger number kyun ($n_1{u}_1=n_2{u}_2$ picture)

Wahi blue bar nahi badlti jab tum measuring tiles switch karte ho. Lekin ek choti tile zyada baar fit hoti hai.

YE KYUN HOTA HAI: actual amount of length product $n\times u$ hai, na sirf $n$ ya $u$. Agar tum $u$ chota karo, toh product fixed rakhne ke liye $n$ barhna chahiye. Ye exactly parent ki equation hai:

3. Bracket notation $[]$ — "ki unit"

Parent $[F]$ aur $[{\text{m s}}^{-2}]$ jaisi cheezein likhta hai. Ye koi naya operation nahi hai — ye shorthand hai.

Hum ise kyun chahte hain: unit derive karte waqt hum "5" ya "72" ki parwah nahi karte; hum sirf standards ko track karte hain. Bracket hume sirf units par algebra karne deta hai.

4. Units par exponents: ${\text{s}}^{-2}$ actually kya kehta hai

Force aane se pehle, tumhe ${\text{s}}^2$ aur ${\text{s}}^{-2}$ se comfortable hona chahiye.

Physics negative-exponent form kyun pasand karta hai: $\text{kg}\text{m}{\text{s}}^{-2}$ ek line par likhne se sab kuch ek single product ban jaata hai, toh neeche wale exponent-arithmetic rules saaf apply hote hain.

5. Base symbols $L,M,T$ (aur baaki chaar)

Ab parent ki table ke letters samajh aate hain.

"Metre" ki jagah letters kyun? Kyunki "speed = length ÷ time" jaisa ek rule tab bhi sach hai chahe koi bhi length-standard use karo. Letter $L$ "length-ness" ko capture karta hai bina metres, feet, ya miles mein commit kiye.

Figure mein LEGO wala idea literally dikhaya gaya hai: teen base bricks ($L$, $M$, $T$) ek saath snap hote hain aur derived words banate hain jaise speed ($L/T$) aur force ($ML/T^2$).

6. Units multiply hoti hain kyunki quantities multiply hoti hain

Ye woh single fact hai jo parent mein har derivation ko power deta hai.

7. Dimensionless quantities — jab units cancel ho jaate hain

Parent ki angle-mistake ke liye ye idea chahiye.

Ye kyun matter karta hai: dimensionless cheezein (angles, refractive index, strain) naye base quantities nahi hain — koi naya measurement nahi hua, bas do lengths ka comparison tha. Jo Vectors tum baad mein miloge, woh isi wajah se freely angles use karte hain.

Prerequisite map

Equipment checklist

Right side cover karo aur aage badhne se pehle khud ko test karo.