Imagine you want to describe anything in physics — speed, force, energy, electric current.
Every such quantity is secretly built from a tiny set of fundamental measuring sticks .
The whole SI system is just the claim: seven base units are enough; *everything else is a
recipe (a product of powers) built from these seven==. If you know the recipe, you never need
to memorise a derived unit — you can derive it.
A measurement is a comparison: "this rod is 3 of something ". That something (the standard)
must be agreed by everyone, or my "3" and your "3" disagree. SI = Système International , the
globally agreed set of standards so a Japanese engineer and a Brazilian physicist mean the
identical thing by "1 metre" or "1 second". The genius move: pick the minimum number of
independent standards, and generate the rest.
Definition The seven SI base units
Base quantity
Symbol
Unit name
Unit symbol
Length
L L L metre m \text{m} m
Mass
M M M kilogram kg \text{kg} kg
Time
T T T second s \text{s} s
Electric current
I I I ampere A \text{A} A
Thermodynamic temperature
Θ \Theta Θ kelvin K \text{K} K
Amount of substance
N N N mole mol \text{mol} mol
Luminous intensity
J J J candela cd \text{cd} cd
WHY these seven and not others? They are chosen to be dimensionally independent : none can be
written as a combination of the others. You cannot build "time" out of length and mass, etc. They
form a basis for the "vector space" of physical dimensions.
Old definitions used physical objects (a metal cylinder = the kilogram). Objects drift, get
scratched, are lost. So in 2019 SI was redefined by fixing constants of nature — these never
change. The trick: fix a constant's numerical value, and the unit falls out.
A derived unit is defined by an equation of physics . Want the unit of force? Take Newton's
law F = m a F=ma F = ma generated .
F = m a ⇒ [ F ] = [ m ] [ a ] = kg ⋅ m s 2 = kg⋅m⋅s − 2 ≡ 1 N F = ma \quad\Rightarrow\quad [F] = [m][a] = \text{kg}\cdot\frac{\text{m}}{\text{s}^2}=\text{kg·m·s}^{-2}\equiv 1\ \text{N} F = ma ⇒ [ F ] = [ m ] [ a ] = kg ⋅ s 2 m = kg⋅m⋅s − 2 ≡ 1 N Why this step? Acceleration is "metres per second, per second" = m/s 2 =\text{m/s}^2 = m/s 2 is the recipe.
W = F ⋅ d ⇒ [ W ] = N⋅m = kg⋅m 2 ⋅s − 2 ≡ 1 J W = F\cdot d \Rightarrow [W]=\text{N·m}=\text{kg·m}^2\text{·s}^{-2}\equiv 1\ \text{J} W = F ⋅ d ⇒ [ W ] = N⋅m = kg⋅m 2 ⋅s − 2 ≡ 1 J Why? Work = force along a distance, so multiply force unit by metre.
P = W t ⇒ [ P ] = J s = kg⋅m 2 ⋅s − 3 ≡ 1 W P=\frac{W}{t}\Rightarrow [P]=\frac{\text{J}}{\text{s}}=\text{kg·m}^2\text{·s}^{-3}\equiv 1\ \text{W} P = t W ⇒ [ P ] = s J = kg⋅m 2 ⋅s − 3 ≡ 1 W
p = F A ⇒ [ p ] = N m 2 = kg⋅m − 1 ⋅s − 2 ≡ 1 Pa p=\frac{F}{A}\Rightarrow[p]=\frac{\text{N}}{\text{m}^2}=\text{kg·m}^{-1}\text{·s}^{-2}\equiv 1\ \text{Pa} p = A F ⇒ [ p ] = m 2 N = kg⋅m − 1 ⋅s − 2 ≡ 1 Pa
Q = I t ⇒ [ Q ] = A⋅s ≡ 1 C Q=It\Rightarrow[Q]=\text{A·s}\equiv 1\ \text{C} Q = I t ⇒ [ Q ] = A⋅s ≡ 1 C V = W Q ⇒ [ V ] = J C = kg⋅m 2 ⋅s − 3 ⋅A − 1 ≡ 1 V V=\frac{W}{Q}\Rightarrow[V]=\frac{\text{J}}{\text{C}}=\text{kg·m}^2\text{·s}^{-3}\text{·A}^{-1}\equiv 1\ \text{V} V = Q W ⇒ [ V ] = C J = kg⋅m 2 ⋅s − 3 ⋅A − 1 ≡ 1 V Why? Charge = current × time (current is charge-per-time). Voltage = energy per unit charge.
Worked example 1 — Find the base-unit form of theohm Ω \Omega Ω V = I R ⇒ R = V / I V=IR\Rightarrow R=V/I V = I R ⇒ R = V / I [ R ] = [ V ] [ A ] = kg⋅m 2 s − 3 A − 1 A = kg⋅m 2 s − 3 A − 2 [R]=\frac{[V]}{[A]}=\frac{\text{kg·m}^2\text{s}^{-3}\text{A}^{-1}}{\text{A}}=\text{kg·m}^2\text{s}^{-3}\text{A}^{-2} [ R ] = [ A ] [ V ] = A kg⋅m 2 s − 3 A − 1 = kg⋅m 2 s − 3 A − 2 Why this step? We already derived the volt; dividing by ampere just lowers the power of A by one.
1 2 m v 2 \tfrac12 mv^2 2 1 m v 2 [ m v 2 ] = kg ⋅ ( m/s ) 2 = kg⋅m 2 s − 2 = J [mv^2]=\text{kg}\cdot(\text{m/s})^2=\text{kg·m}^2\text{s}^{-2}=\text{J} [ m v 2 ] = kg ⋅ ( m/s ) 2 = kg⋅m 2 s − 2 = J Why? The pure number 1 2 \tfrac12 2 1
Worked example 3 — Unit of the gravitational constantG G G F = G m 1 m 2 r 2 ⇒ G = F r 2 m 1 m 2 F=\dfrac{Gm_1m_2}{r^2}\Rightarrow G=\dfrac{Fr^2}{m_1m_2} F = r 2 G m 1 m 2 ⇒ G = m 1 m 2 F r 2 [ G ] = N⋅m 2 kg 2 = kg⋅m⋅s − 2 ⋅ m 2 kg 2 = m 3 kg − 1 s − 2 [G]=\frac{\text{N·m}^2}{\text{kg}^2}=\frac{\text{kg·m·s}^{-2}\cdot\text{m}^2}{\text{kg}^2}=\text{m}^3\text{kg}^{-1}\text{s}^{-2} [ G ] = kg 2 N⋅m 2 = kg 2 kg⋅m⋅s − 2 ⋅ m 2 = m 3 kg − 1 s − 2 Why? Rearrange the law to isolate G G G
Common mistake "The kilogram is thegram with a prefix, so the base unit is the gram."
Why it feels right: every other base unit is prefix-free (metre, second), so it seems
inconsistent that the kilo gram is base. Fix: historically yes, but officially the
kilogram (with the kilo) is the SI base unit of mass. Prefixes still attach to gram for
naming (milligram), but the standard is the kg.
Common mistake "Temperature in °C is an SI unit."Why it feels right: Celsius is everywhere in daily life. Fix: the SI base unit is the
kelvin ; °C is a derived convenience scale (T ° C = T K − 273.15 T_{°C}=T_K-273.15 T ° C = T K − 273.15 size of
degree but a shifted zero.
Common mistake "Newton is a base unit because it's so fundamental."Why it feels right: force feels primary in mechanics. Fix: force is derived from
F = m a F=ma F = ma
amount of substance (mol) with mass (kg) .
Why it feels right: both feel like "how much stuff". Fix: mole counts number of
entities (N A N_A N A
Recall Feynman: explain to a 12-year-oldImagine a LEGO set with only 7 special starter bricks : a ruler-brick (metre), a weight-brick
(kilogram), a clock-brick (second), an electricity-brick (ampere), a hotness-brick (kelvin), a
counting-brick (mole), and a brightness-brick (candela). Every other measuring tool — for
speed, push, energy, anything — is just these 7 bricks snapped together in some pattern. So you
never have to invent a new brick; you just look at the science equation and snap the right
starter bricks together.
"Mrs. KAT Makes Cool Juice" for the seven units:
M etre, k ilogr am... use the line:
"Mary's Kind Sister Always Keeps Many Candles" →
M etre, K ilogram, S econd, A mpere, K elvin, M ole, C andela.
#flashcards/physics
How many SI base units are there? Seven.
Name the seven SI base units. metre, kilogram, second, ampere, kelvin, mole, candela.
SI base unit of electric current? ampere (A).
SI base unit of amount of substance? mole (mol).
SI base unit of luminous intensity? candela (cd).
Base-unit form of the newton? kg⋅m⋅s − 2 \text{kg·m·s}^{-2} kg⋅m⋅s − 2 (from
F = m a F=ma F = ma ).
Base-unit form of the joule? kg⋅m 2 ⋅s − 2 \text{kg·m}^2\text{·s}^{-2} kg⋅m 2 ⋅s − 2 (from
W = F d W=Fd W = F d ).
Base-unit form of the watt? kg⋅m 2 ⋅s − 3 \text{kg·m}^2\text{·s}^{-3} kg⋅m 2 ⋅s − 3 (from
P = W / t P=W/t P = W / t ).
Base-unit form of the pascal? kg⋅m − 1 ⋅s − 2 \text{kg·m}^{-1}\text{·s}^{-2} kg⋅m − 1 ⋅s − 2 (from
p = F / A p=F/A p = F / A ).
Base-unit form of the volt? kg⋅m 2 ⋅s − 3 ⋅A − 1 \text{kg·m}^2\text{·s}^{-3}\text{·A}^{-1} kg⋅m 2 ⋅s − 3 ⋅A − 1 (from
V = W / Q V=W/Q V = W / Q ).
Base-unit form of the ohm? kg⋅m 2 ⋅s − 3 ⋅A − 2 \text{kg·m}^2\text{·s}^{-3}\text{·A}^{-2} kg⋅m 2 ⋅s − 3 ⋅A − 2 (from
R = V / I R=V/I R = V / I ).
What constant defines the metre? speed of light
c = 299 792 458 m/s c=299\,792\,458\,\text{m/s} c = 299 792 458 m/s .
What constant defines the kilogram (2019)? Is the newton a base or derived unit? Derived (from
F = m a F=ma F = ma ).
Units of G G G m 3 kg − 1 s − 2 \text{m}^3\text{kg}^{-1}\text{s}^{-2} m 3 kg − 1 s − 2 .
Relation between °C and K? T ° C = T K − 273.15 T_{°C}=T_K-273.15 T ° C = T K − 273.15 (same degree size, shifted zero).
dimensionally independent
combined via physics eqns
ampere, kelvin, mole, candela
Fixed constants of nature
Intuition Hinglish mein samjhoDekho, SI units ka pura idea bahut simple hai: poore physics mein sirf saat base units hain —
metre, kilogram, second, ampere, kelvin, mole, candela. Inko "base" isliye kehte hain kyunki ye ek
dusre se banaye nahi ja sakte; ye independent measuring sticks hain. Baaki sab cheezein — force,
energy, power, voltage — in saaton ko mila ke banti hain, aur unko hum derived units kehte hain.
Sabse important baat: derived unit ko ratta maarne ki zaroorat nahi! Bas us quantity ka physics
equation pakdo. Jaise force ke liye F = m a F=ma F = ma newton . Energy ke
liye W = F d W=Fd W = F d joule . Power ke liye P = W / t P=W/t P = W / t watt . Equation hi recipe hai.
Ek confusion clear kar lo: kilogram base unit hai (kilo ke saath), gram nahi. Aur temperature ka
SI base unit kelvin hai, Celsius nahi — Celsius bas shifted scale hai (K − 273.15 K - 273.15 K − 273.15 c c c h h h
Exam mein "is unit ka base form likho" type questions aate hain — wahan ghabraana mat. Equation
likho, har quantity ka base unit substitute karo, powers add/subtract karo, answer aa jaayega. Yahi
80/20 hai: 7 bricks + equations = sab kuch derive ho jaata hai.
