1.1.1
Physics essentially measure karne ka kaam hai. Lekin har cheez ko scratch se measure nahi kar sakte — woh circular ho jaata. Isliye hum ek chhoti si "starter" quantities ki list chunte hain (fundamental quantities ), har ek ke liye ek unit par agree karte hain, aur phir baaki sab kuch (derived quantities ) unhe multiply aur divide karke banate hain. Yeh ek language ki tarah hai: kuch letters milke infinitely many words bana dete hain.
Definition Physical quantityPhysical quantity nature ki koi bhi aisi property hai jo measure ki ja sake aur number × unit ke roop mein express ki ja sake.
Physical quantity = { numerical value } × [ unit ] 5 m
Number AUR unit kyun? Akela "5" meaningless hai — 5 kya? Seconds? Kilograms? Unit batata hai ki aapne kis standard se compare kiya, aur number batata hai ki us standard ki kitni copies fit hoti hain.
Intuition Number aur unit inversely linked hainEk hi physical length ko 2 m 200 cm n 1 u 1 = n 2 u 2 invariant hai; wahi poori quantity hai.
Definition Fundamental (base) quantitiesWoh quantities jo independent building blocks ki tarah chunni jaati hain — inhe kisi aur quantity ke terms mein define nahi kiya jaata. SI mein seven hain:
Quantity
Symbol
SI Unit
Unit symbol
Length
L metre
m
Mass
M kilogram
kg
Time
T second
s
Electric current
I A ampere
A
Temperature
Θ kelvin
K
Amount of substance
N mole
mol
Luminous intensity
J candela
cd
Definition Derived quantitiesWoh quantities jo fundamental ones ko multiply/divide (aur powers) karke banayi jaati hain. Inke units base units ke products/quotients hote hain.
e.g. speed = time length ⇒ [ m s − 1 ]
Sirf seven kyun? Kyunki seven minimum set hai jo (a) independent hai — koi ek doosre se nahi ban sakta — aur (b) sufficient hai — har known quantity inse reach ki ja sakti hai. Kam hote toh gaps rehte; zyada hote toh redundant hota.
Worked example Worked example 2 — Pressure ki unit (Pascal)Pressure = area force
Kyun? Pressure define hota hai force ko area par spread karke.
[ P ] = [ area ] [ F ] = m 2 kg m s − 2 = kg m − 1 s − 2 ≡ 1 Pa m / m 2 = m − 1 1 − 2 = − 1
Worked example Worked example 3 — Derived quantity convert karna72 km h − 1 m s − 1 72 h km × 1 km 1000 m × 3600 s 1 h = 72 × 3600 1000 m s − 1 = 20 m s − 1 Yeh fractions chain kyun karte hain? Har fraction 1 ke barabar hai (top = bottom real value mein), isliye multiply karne se quantity nahi badalti — sirf units relabel hote hain.
Common mistake "Angle aur Celsius mein temperature bhi fundamental hain, na?"Kyun sahi lagta hai: angle clearly "kuch measureable" hai, aur Celsius har thermometer par hota hai.
Sahi answer: Angle (radian) ek ratio hai arc/radius = length/length — yeh dimensionless hai, ek derived (supplementary) quantity, base nahi. Celsius SI base unit nahi hai; kelvin hai, kyunki base scale absolute hona chahiye (true zero se start) taaki ratios ka matlab ho.
Common mistake "Weight aur mass ek hi fundamental quantity hain."Kyun sahi lagta hai: rozmarra ki zindagi mein hum kehte hain "mera weight 60 kg hai".
Sahi answer: Mass (kg) fundamental hai — matter ki matra. Weight ek force hai W = m g derived quantity. Wahi object, Moon par alag mass-vs-weight.
Common mistake "Zyada base units = zyada powerful physics."Kyun sahi lagta hai: zyada tools sunne mein better lagte hain.
Sahi answer: Base set minimal aur independent hona chahiye. Agar "speed" ko base unit banao, toh woh length÷time se clash karega — ek hi cheez ki do incompatible definitions. Redundancy consistency tod deti hai.
Recall Pehle khud try karo
Har physical quantity ke saath unit kyun honi chahiye?
Saaton SI base quantities apne units ke saath list karo.
Joule ke base units first principles se derive karo.
Kya angle fundamental hai ya derived? Kyun?
n 1 u 1 = n 2 u 2
(Answers poori note mein hain — band karo aur reconstruct karo.)
Recall Feynman: ek 12-saal ke bachche ko explain karoSocho tumhare paas sirf teen measuring tools hain: ek ruler (length), ek kitchen scale (mass), aur ek stopwatch (time). Sirf inhi se tum pata kar sakte ho ki car kitni fast jaati hai (length ÷ time), koi cheez push karne mein kitni force lagti hai (mass × speed kitni fast badhti hai), aur ek punch mein kitni energy hai. Tumhe kabhi koi special "energy ruler" nahi chahiye tha — tumne energy ko teen simple tools se banaya . Saaton SI base units bas duniya ke official "simple tools" hain, aur physics ki baaki sab cheez inhe LEGO ki tarah combine karke banti hai.
Mnemonic Saaton base units"Lovely Mary Took A Tasty Mango (in) Candlelight"
L ength · M ass · T ime · A mpere · T emperature · M ole · C andela.
A physical quantity is expressed as ek numerical value × ek unit
How many SI base (fundamental) quantities are there? Seven
Name the seven SI base quantities length, mass, time, electric current, temperature, amount of substance, luminous intensity
SI unit of luminous intensity candela (cd)
SI unit of amount of substance mole (mol)
Define a derived quantity woh quantity jo fundamental quantities ko multiplication/division (aur powers) se banai jaati hai
Base units of force (newton) kg m s⁻² (F = ma se)
Base units of energy (joule) kg m² s⁻² (W = F·d se)
Base units of pressure (pascal) kg m⁻¹ s⁻² (P = F/area se)
Why is an angle dimensionless? yeh arc length ÷ radius = length/length hai, isliye units cancel ho jaate hain
Relation between number and unit for a fixed quantity n₁u₁ = n₂u₂ (chhota unit ⇒ bada number)
Is mass or weight fundamental? mass fundamental hai (kg); weight ek derived force hai (W = mg, N mein)
Convert 72 km/h to m/s 20 m/s
Why exactly seven base quantities? minimal set jo independent bhi hai aur baaki sab banane ke liye sufficient bhi
independent and sufficient
