The complete lecture — every idea comes alive in the live panel on the right as you read. Scroll down; the animation keeps pace, and in the calipers section you can slide the real 3D instrument yourself.
1 — Physics & physical quantities
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 have no unit, so they are not physical quantities.
- Base quantities (7) — length (m), mass (kg), time (s), current (A), temperature (K), amount of substance (mol), luminous intensity (cd).
- Derived quantities — built by × and ÷ of base ones: speed (m/s), force (kg·m/s² = N), pressure (Pa), energy (J).
Exam point: the kilogram is the only base unit whose name carries a prefix (kilo).
2 — Scientific notation & SI prefixes
Physics spans 10⁻¹⁵ m (a nucleus) to 10²¹ m (a galaxy). Scientific notation keeps one non-zero digit before the point: 384 000 000 m = 3.84 × 10⁸ m.
Prefixes to memorisepico 10⁻¹² · nano 10⁻⁹ · micro 10⁻⁶ · milli 10⁻³ · centi 10⁻²
kilo 10³ · mega 10⁶ · giga 10⁹ · tera 10¹²
So 0.00000052 m = 5.2 × 10⁻⁷ m = 520 nm, and 3.6 MJ = 3.6 × 10⁶ J. Use only one prefix at a time — 1 pF, never 1 μμF.
3 — Dimensions of physical quantities
The dimension writes a quantity in terms of mass [M], length [L] and time [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. Pure numbers (½, π) are dimensionless.
4 — Checking & deriving with dimensions
check — v = u + at
[v] = [LT⁻¹] · [u] = [LT⁻¹] · [at] = [LT⁻²][T] = [LT⁻¹] → consistent ✓
derive — pendulum period
Assume T ∝ lᵃgᵇ.
[T] = [L]ᵃ[LT⁻²]ᵇ → b = −½, a = +½ → T = 2π√(l/g) (2π from experiment)
Limitations: cannot find constants like 2π, cannot check sums of unlike terms or trig/log relations.
5 — Significant figures & rounding
- Significant — non-zero digits; zeros between digits (7.04); trailing zeros after a decimal (2.500).
- Not significant — leading zeros (0.0046 → 2 s.f.); trailing zeros of a bare whole number (4500) are ambiguous — fix with 4.5 × 10³.
Operations× ÷ → keep least s.f. · + − → keep least decimal places
round a final 5 to the even digit: 7.35 → 7.4, 7.45 → 7.4
example
12.42 cm × 3.2 cm = ?
39.744 → least s.f. is 2 → 40 cm²
6 — Errors & uncertainties
- Random error — readings scatter both sides of the true value. Cure: repeat and average.
- Systematic error — every reading shifted the same way (zero error, slow clock). Cure: find and correct — averaging never helps.
Uncertaintyx = (5.2 ± 0.1) cm · fractional = Δx/x · percentage = (Δx/x)×100%
± for sums · add %ages for × ÷ · ×n for powers (V = L³ → 3× %age of L)
example
30 vibrations take (54.6 ± 0.1) s. T?
T = 1.82 s, %age = 0.1/54.6 ≈ 0.2% — timing many swings shrinks the error.
7 — Least count
The least count (LC) is the smallest reading an instrument can make. A tailor's tape (1 mm at best) fits a kameez; a phone's glass needs a screw gauge reading 0.01 mm.
The precision laddermetre rule → LC 1 mm
vernier calipers → LC 0.1 mm
screw gauge → LC 0.01 mm
A single reading is quoted as ± one least count: (2.32 ± 0.01) cm.
8 — Vernier calipers (board practical)
A main scale in mm plus a sliding vernier scale: 10 divisions covering only 9 mm. The mismatch reads tenths of a millimetre.
Vernier formulasLC = 1 MSD − 1 VSD = 1 − 0.9 = 0.1 mm = 0.01 cm
reading = main scale + (coinciding division × LC)
corrected = observed − zero error (with sign)
worked reading
Main scale 2.3 cm, 4th division coincides, zero error +0.02 cm.
observed = 2.3 + 4×0.01 = 2.34 cm → corrected = 2.34 − 0.02 = 2.32 cm
9 — Screw gauge (micrometer)
A precise screw advances one pitch per rotation; the circular scale slices that pitch into hundredths.
Screw gauge formulasLC = pitch / circular divisions = 1 mm / 100 = 0.01 mm
reading = sleeve reading + (circular division × LC)
worked reading
Wire: sleeve 3.5 mm, 24th division on the line, zero error −0.03 mm.
observed = 3.5 + 24×0.01 = 3.74 mm → corrected = 3.74 + 0.03 = 3.77 mm
Ratchet: the clicking cap applies the same pressure every time — it removes a squeeze-type systematic error.
10 — Worked numericals & exam recap
numerical — uncertainty in V = L³
L = (2.00 ± 0.02) cm.
%age in L = 1% → %age in V = 3% → V = (8.00 ± 0.24) cm³
numerical — sig-fig addition
72.1 + 3.42 + 0.003 g?
75.523 → least decimal places = 1 → 75.5 g
- Physical quantity = number × unit; 7 base → all derived.
- Scientific notation d.dd × 10ⁿ; prefixes pico → tera.
- Homogeneity checks equations; dimensions derive T = 2π√(l/g).
- Sig figs: ×/÷ least s.f., +/− least decimal places.
- Random → average; systematic → correct the cause.
- LC: rule 1 mm, vernier 0.1 mm, screw gauge 0.01 mm; corrected = observed − zero error.