Chapter 1: Physical Quantities, Units and Measurement
Objectives
Candidates should be able to:
- show understanding that all physical quantities consist of a numerical magnitude and a unit
- recall the following base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
- use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units: nano (n), micro (µ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G)
- show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth
- state what is meant by scalar and vector quantities and give common examples of each
- add two vectors to determine a resultant by a graphical method
- describe how to measure a variety of lengths with appropriate accuracy by means of tapes, rules, micrometers and calipers, using a vernier scale as necessary
- describe how to measure a short interval of time including the period of a simple pendulum with appropriate accuracy using stopwatches or appropriate instruments
1.1 Physical Quantities and SI Units
- Physical quantities consist of:
- Numerical magnitude – denotes the size of the physical quantity.
- Unit – denotes the physical quantity it is expressing.
- Physical quantities can be classified into:
- Basic quantities
Basic Quantity Name of SI Unit SI Unit length metre m mass kilogram kg time second s thermodynamic temperature kelvin K amount of substance mole mol - Derived quantities – defined in terms of the basic quantities through equations. SI units for these quantities are obtained from the basic SI units through the equations.
Example 1.1
- Basic quantities
- Units of measurements: SI units are used as standardised units in all measurements in the world. SI is the short form for “International System of Units”.
- Other Units:
Length Mass Time 1 km = 1000 m 1 kg = 1000 g 1 h = 60 min 1 m = 100 cm 1 g = 1000 mg 1 min = 60 s 1 cm = 10 mm
- Examples of some derived quantities and their units:
Derived Quantity SI Unit area m2 volume m3 density kg/m3 speed m/s A complete list of key quantities, symbols and units used for the O Level examination can be found in the syllabus.
1.2 Prefixes, Symbols and Orders of Magnitude
- Physical quantities can be very large, like 23 150 000 000 m, or very small, like 0.000 000 756 m. Writing down such numbers can be time consuming and error-prone. We use prefixes to indicate decimal sub-multiples and multiples of the SI units to make writing such numbers easier.
- Some prefixes of the SI units are as follows:
Prefix Multiple Symbol Factor Order of Magnitude Tera 1 000 000 000 000 T 1012 12 Giga 1 000 000 000 G 109 9 Mega 1 000 000 M 106 6 Kilo 1000 K 103 3 Deci 0.1 d 10-1 -1 Centi 0.01 c 10-2 -2 Milli 0.001 m 10-3 -3 Micro 0.000 001 μ 10-6 -6 Nano 0.000 000 001 n 10-9 -9 Pico 0.000 000 000 001 p 10-12 -12 The ones in bold are specifically required in the syllabus.
Example 1.2- 0.000 0031 m = 3.1 μm = 3.1 * 10-6m
- 0.000 000 0012 s = 1.2 ns = 1.2 * 10-9s
- When measurements are too large or too small, it is convenient to express them in standard form as follows:
M × 10N
M lies in the range of: 1 ⩽ M < 10
N denotes the order of magnitude and is an integer. - Orders of magnitude are often being used to estimate numbers which are extremely large to the nearest power of ten.
E.g.- Estimate the number of strands of hair on a person’s head.
- Estimate the number of breaths of an average person in his lifetime.
- The following tables show how the orders of magnitude are used to compare some masses and lengths.
Mass/kg Factor Electron 10-30 Proton 10-27 Ant 10-3 Human 101 Earth 1024 Sun 1030 Length/m Factor Radius of a proton 10-15 Radius of an atom 10-10 Height of an ant 10-3 Height of a human 100 (100 = 1) Radius of the Earth 107 Radius of the Sun 109 Example 1.3
Find the ratio of the height of a human to that of an ant.
Ratio of height of human to that of an ant = 100/10-3 = 103 = 1000.
