SI units — seven base units and all derived units: Foundations

1.1.2 · D1 · Physics › Measurement, Vectors & Kinematics › SI units — saat base units aur saare derived units

Pehla split: quantity vs unit vs number

Topic ko ye kyun chahiye. Jab parent kehta hai "saat base units", iska matlab hai saat agreed standard chunks. Jab kehta hai "saat base quantities", iska matlab hai saat tarah ki cheezein jo un chunks se measure hoti hain. Dono ko confuse karo to poori table bakwaas lagegi. Figure dekho: coloured chunk unit hai, chunks ki count number hai, aur ruler khud quantity hai.

Har recipe ka symbol: powers

Force ya energy se pehle, tumhe $s^{- 2}$ aur $m^{2}$ jaisi expressions padhni aani chahiye.

Topic ko ye kyun chahiye. Force ka base unit $kg\cdotm\cdots^{- 2}$ likha jaata hai. Woh $s^{- 2}$ decoration nahi hai — iska literally matlab hai "second se divide karo, phir dobara second se divide karo". Parent ki poori table saat sticks ki powers hai; agar tum negative exponent nahi padh sakte, to ek bhi derived unit nahi padh sakte.

Ratio: "per" ka asli matlab

Topic ko ye kyun chahiye. Lagbhag har derived unit ek "per" hai: speed is m per s, pressure is force per area, voltage is energy per charge. "Per" word woh engine hai jo powers ko stack karta hai. Figure dekho — wahi journey "ek second mein kitni door" ke roop mein padhna ratio deta hai; woh ratio hi derived unit hai.

Bracket notation: $[\cdot]$ ka matlab "ki units"

Topic ko ye kyun chahiye. Parent likhta hai $[F] = [m] [a]$ . Ye master move hai: units usi tarah multiply hoti hain jaise physics equation multiply hoti hai. Agar $F = ma$ hai, to $[F] = [m] \cdot [a]$ hai. Brackets tumhe numbers chhod ke sirf sticks track karne dete hain. Ye Dimensional Analysis ka seed hai.

"Basis" ka idea: exactly saat kyun

Topic ko ye kyun chahiye. Parent claim karta hai saat minimum complete set hai. "Complete" = har quantity reachable hai; "minimum" = koi ek nahi chhor sakte. Ye exactly basis ki definition hai. Figure dekho: teen independent arrows room mein har jagah pahunch sakte hain; ek fourth arrow jo usi room mein ho woh redundant hoga — pehle teen se mix ho jaata.

Powers-of-ten aur prefixes (kilogram mein kilo)

Topic ko ye kyun chahiye. Parent ki ek sachchi oddity ye hai ki mass ka base unit kilogram hai, gram nahi. Ek prefix base unit ke naam mein baka hua hai. Tumhe prefix ko sirf ek number multiplier dekhna hoga taaki tum maan sako ki $kg$ (na ki $g$ ) official stick hai.

Ye sab topic mein kaise feed hota hai

Baayein taraf ka har foundation "derive any unit" box se pehle solid hona chahiye — aur woh box hi parent topic hai. Bracket notation Dimensional Analysis ka darwaza bhi kholti hai, aur base quantities length/time Kinematics — velocity and acceleration, Newton's Laws of Motion aur Work, Energy and Power mein har jagah dubara aati hain.

Worked micro-example: zero se speed unit banana

Equipment checklist

Khud test karo — har ek ka jawab turant "haan" hona chahiye.

Mein "

5 kg

" mein number, unit, aur quantity bata sakta hoon.

number

= 5

, unit

=

kilogram, quantity

=

mass.

Mein

s^{- 2}

ko seedhi bhasha mein padh sakta hoon.

"divided by second, squared" yaani

1/ s^{2}

Mujhe pata hai

x^{0}

kya hota hai.

1

Mein "metres per second" ko power expression mein badal sakta hoon.

m\cdots^{- 1}

Mujhe pata hai bracket

[F]

ka matlab kya hai.

F

ki units (dimension)".

Mein woh rule bata sakta hoon jo

F = ma

ko units se jodata hai.

[F] = [m] [a]

— units usi tarah multiply hoti hain jaise equation hoti hai.

Mein bata sakta hoon exactly saat base units kyun hain.

ye independent hain (koi doosron se nahi banta) aur complete hain (baaki sab mix ho sakte hain) — ek basis.

Mujhe pata hai kilogram kyun, gram nahi, base hai.

officially kilogram SI base unit of mass hai; prefix baka hua hai.

Mujhe pata hai prefix size change karta hai, quantity ki tarah nahi.

haan — kilometre aur metre dono length measure karte hain.

Recall Ek-line summary

Powers, ratios, aur bracket $[\cdot]$ padhna seekho, saath mein basis ka idea "saat independent sticks", aur parent topic pure bookkeeping ban jaata hai.