Physics 1st Paper · Classes 11-12 · Chapter 1 · 1.6

Fundamental and Derived Units.

The metre needs no help to be a metre. The newton does: you need the kilogram, the metre and the second to build it. This note teaches you to tell the units that stand alone from the ones built on top of them.

1. Three kinds of unit

Units come in three kinds: fundamental (or primary), derived (or compound) and practical. A unit that leans on no other unit, one that stands completely on its own, is a fundamental unit.

In mechanics there are three: the units of length, mass and time. Each must be definite, convenient and unchanging. The S.I. system has more base units, and you will meet them shortly.

A unit built from the fundamental units is a derived unit: m² for area, and the units of volume, velocity, acceleration and force. When a fundamental unit is too large or too small, a multiple or sub-multiple of it is taken as the unit. That is a practical unit: km, micron (μ), ton.

Build derived units yourself from three bricks, kg, m and s. Raise or lower each power and see what you made.

The light-year has the same dimension as length. For that reason the book's inquiry task calls the light-year a primary unit.

2. Systems and the nine quantities

The 1960 rules for writing units are these. Write the unit in the singular (km, not kms). Put no full stop after it. Write Nm⁻² rather than N/m². And in a long number, group the digits in threes on both sides of the decimal point, as in 24,765·321.

In the C.G.S system the units of length, mass and time are the centimetre, gram and second. It is also called the metric or French system, and it is a decimal system. In the M.K.S system the same three are measured in the metre, kilogram and second.

The International System of Units, S.I. for short, came into use in 1960. It has nine quantities in all.

The nine quantities and units: length metre (m), mass kilogram (kg), time second (s), temperature kelvin (K), electric current ampere (A). Angle comes in two kinds: plane angle in the radian (rad), solid angle in the steradian (sr). Then luminous intensity in the candela (cd) and amount of substance in the mole (mol). Match the pairs.

Derived units and their symbols: force newton (N), energy joule (J), power watt (W), charge coulomb (C), resistance ohm (Ω), potential volt (V), frequency hertz (Hz).

The M.K.S.A system has four standard units: the metre, kilogram, second and ampere.

Take a bar of an alloy of 90% platinum and 10% iridium. The distance between two marks on it is the international metre, and the bar is kept at 0°C. One hundredth of it is a centimetre.

3. Lengths from small to large

The small units: 1 X.U. (X-ray unit) = 10⁻¹³ m; 1 Å (angstrom) = 10⁻¹⁰ m; 1 mμ (millimicron) = 10⁻⁹ m; 1 μ (micron) = 10⁻⁶ m; 1 Mm (megametre) = 10⁶ m.

For the scale of space there are the astronomical units: 1 AU = 1.495×10¹¹ m. 1 light-year = 9.42×10¹⁵ m, the distance light travels in a year. The accepted value is 9.46×10¹⁵ m, and options often give it as 9.4×10¹² km. 1 parsec = 3.26 light-years = 3.083×10¹⁶ m. So the parsec is larger than the light-year.

For the mass of atoms there is the atomic mass unit: 1 a.m.u. = 1.66×10⁻²⁷ kg.

Before you sort them, climb the ladder: from the femtometre to the parsec, and how many times bigger each rung is.

Now put the units in order yourself, smallest first.

4. Prefixes

Sub-multiple prefixes, the ones that shrink a unit: deci d 10⁻¹; centi c 10⁻²; milli m 10⁻³; micro μ 10⁻⁶; nano n 10⁻⁹; pico p 10⁻¹²; femto f 10⁻¹⁵; atto a 10⁻¹⁸.

Multiple prefixes, the ones that enlarge a unit: deca da 10¹; hecto h 10²; kilo k 10³; myria Ma 10⁴; mega M 10⁶; giga G 10⁹; tera T 10¹²; peta P 10¹⁵; exa E 10¹⁸.

5. Conversions at work

Walk through the first two conversions of the book's Example 1.1: ton to kilogram, then gallon to cubic metre.

To write the unit of force in base units, start from F = ma. The unit of m is kg and the unit of a is ms⁻², so the unit of force is kg ms⁻² (Dhaka Board 2015).

1 mile = 1760×3×12×2.54 cm = 1.609 km. So 1 mile − 1 km = 0.609 km = 609 m.

If 10 amu equals the mass of n electrons, then with 1 amu = 1.66×10⁻²⁷ kg and an electron mass of 9.1×10⁻³¹ kg, n = 10×1.66×10⁻²⁷ / 9.1×10⁻³¹ = 1.82×10⁴.

6. Check yourself

Three questions in the exam's style. Start with the first.

Now the second.

And the last.

The whole note on seven cards.

Source: Physics 1st Paper, Classes 11-12 (NCTB), Chapter 1 “Physical World and Measurement”, section 1.6.