Physical quantities and SI units
A number and a unit
How long is a cricket pitch? How heavy is the ball? How long does one over take? Every answer is a number with a unit.
Anything in physics that we can measure is called a physical quantity: length, mass, time, speed, force and many more.
To measure a quantity, we compare it with a fixed standard called a unit. Watch a one-metre rod being laid along the pitch again and again. It fits about twenty times.
So the pitch is about 20 metres long. The number 20 alone means nothing. “20 metres” tells you everything.
A few quantities are chosen as the base, or fundamental, quantities. Their units are called base units.
Every other quantity is built from them. Speed is length divided by time, so its unit is metre per second. Units like this are called derived units.
Watch the unit blocks combine: area is metre times metre, volume is metre cubed, and force turns out to be kilogram metre per second squared.
The full set of base units and derived units is called a system of units. Older systems used centimetres and grams, or feet and pounds.
Today the whole world uses one system: the International System of Units, called SI for short.
The seven SI base units
SI has just seven base quantities, each with its own base unit. Let’s flip the cards over one by one.
Length in metres, m. Mass in kilograms, kg. Time in seconds, s.
Electric current in amperes, A. Thermodynamic temperature in kelvin, K.
Amount of substance in moles, mol. And luminous intensity, how bright a light source is, in candela, cd.
Each base unit is now defined using a fixed constant of nature. The metre, for example, is fixed by the speed of light, so a metre in Chennai is exactly the same as a metre on Mars.
Look at the symbols. A unit named after a scientist gets a capital letter, like A for Ampère or K for Kelvin. We never add a full stop or an “s”: write 5 kg, not 5 kgs.
SI also has two units for angles. Draw an arc of length ds on a circle of radius r. The plane angle is dθ = ds / r, measured in radians.
Now draw a cone from the centre of a sphere, cutting out a patch of area dA. The solid angle is dΩ = dA / r², measured in steradians.
Finally, prefixes handle very big and very small numbers: kilo is a thousand, milli a thousandth, micro a millionth and nano a billionth. Let’s explore the universe with them.
Try it: from a proton to the universe
- Move the slider, or click a dot on the ruler, to jump between objects.
- Each tick on the ruler is ten times the one before it.
- Switch to Masses: prefixes like milli and micro go on the gram, not the kilogram.
Quick check
Which of these is NOT an SI base unit?
- kelvin
- candela
- newton
- mole
Answer
C. The seven base units are the metre, kilogram, second, ampere, kelvin, mole and candela. The newton is a derived unit: 1 N = 1 kg m s⁻².
Prefix practice
A human hair is about 70 µm thick. What is this in metres?
- 7 × 10⁻³ m
- 7 × 10⁻⁵ m
- 7 × 10⁻⁶ m
- 7 × 10⁻⁸ m
Answer
B. Micro (µ) means 10⁻⁶. So 70 µm = 70 × 10⁻⁶ m = 7 × 10⁻⁵ m.
Summary
- A measurement:
quantity = number × unit - Plane angle (radian):
dθ = ds / r - Solid angle (steradian):
dΩ = dA / r²
- SI has seven base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd).
- All other units are derived units, built from the base units. For example, 1 N = 1 kg m s⁻².
- The radian and steradian measure angles. They are ratios, so they have no dimensions.
- Prefixes such as k (10³), m (10⁻³), µ (10⁻⁶) and n (10⁻⁹) keep very large and very small numbers easy to read.