The full, readable lecture — base & derived units, scientific notation, dimensions, significant figures, errors and the two board-practical instruments. As you scroll, the live panel on the right shows each idea through a familiar real-world object: a tailor's tape and lab calipers, a screw gauge on a wire, a kitchen scale, a balance and a dartboard. SI units throughout. Press ▶ to let it read and animate itself, section by section.
Physics studies matter and energy through measurement. A physical quantity is anything expressible as a number × unit — length 5 m, mass 60 kg. Beauty and honesty carry no unit, so they are not physical quantities.
| Base quantity | SI unit | Symbol |
|---|---|---|
| length | metre | m |
| mass | kilogram | kg |
| time | second | s |
| electric current | ampere | A |
| temperature | kelvin | K |
On the right, watch the base-unit tiles slide together: a metre, a kilogram and two seconds combine into kg·m·s⁻² — the newton. Every derived SI unit is just these tiles, multiplied and divided.
Significant figures are the digits a measurement really knows — the reliable ones plus the first doubtful digit. A grocer's digital kitchen scale that reads to 0.001 kg can honestly quote three or four significant figures, no more.
On the right, the scale's display rounds 0.2845 kg down to the digits it can trust — the panel highlights each kept digit in gold.
Physics spans the nucleus (~10⁻¹⁵ m) to a galaxy (~10²¹ m). Scientific notation keeps one non-zero digit before the point: 384 000 000 m = 3.84 × 10⁸ m (Earth–Moon distance).
| Prefix | Symbol | Factor | Prefix | Symbol | Factor |
|---|---|---|---|---|---|
| nano | n | 10⁻⁹ | kilo | k | 10³ |
| micro | μ | 10⁻⁶ | mega | M | 10⁶ |
| milli | m | 10⁻³ | giga | G | 10⁹ |
| centi | c | 10⁻² | tera | T | 10¹² |
So 0.00000052 m = 5.2 × 10⁻⁷ m = 520 nm, and 3.6 MJ = 3.6 × 10⁶ J. On the right a single slider climbs the ladder, snapping a real object onto each rung — virus, blood cell, ant, student, city. Use only one prefix at a time: 1 pF, never 1 μμF.
The dimension of a quantity says which base quantities build it, with what powers, using [M], [L], [T]: velocity [LT⁻¹], acceleration [LT⁻²], force [MLT⁻²], work [ML²T⁻²], pressure [ML⁻¹T⁻²].
The principle of homogeneity: an equation can be correct only if every term has the same dimensions — you can never add a length to a time, just as a balance can never weigh apples against minutes.
On the right, the two pans carry the dimensions of each side. When both read [LT⁻¹] the beam is level; feed it a wrong equation and the heavier side tips. Limitations: dimensions cannot find 2π or ½, nor check trig/log relations.
No measurement is exact. The error is the gap between measured and true value; the uncertainty is the range the true value probably lies in. A dartboard tells the two errors apart at a glance.
On the right, gold darts land all round the bullseye (random, mean ≈ centre); blue darts land tight but high-and-right (systematic) — exactly the picture you see when you throw at a board.
The least count (LC) is the smallest reading an instrument can make. But even a fine instrument lies if its zero is wrong. Picture a school ruler with the first 3 mm snapped off: it now starts at 3 mm, so every length you read is 3 mm too big — a textbook systematic (zero) error.
A single reading is quoted as ± one least count: (2.32 ± 0.01) cm. On the right, the broken ruler measures a pencil: the panel shows the wrong observed value, then subtracts the +3 mm offset to recover the true length — averaging would never have caught it.
A tailor's cloth tape reads your shoulder to about a millimetre — fine for a kameez. But a coin's thickness needs vernier calipers: a main scale in mm plus a sliding vernier of 10 divisions covering only 9 mm. That mismatch reads tenths of a millimetre.
On the right, the jaws glide shut on a coin while the live reading climbs digit by digit — the precision the cloth tape simply cannot reach.
For a wire, paper or phone glass we need hundredths of a millimetre. A screw gauge advances one pitch per full turn; a 100-division circular scale slices that pitch into hundredths.