JPJC 2026 Quantities and Measurement Lecture Notes - Tutors

1 JURONG PIONEER JUNIOR COLLEGE 9478 H2 PHYSICS/8867 H1 PHYSICS QUANTITIES AND MEASUREMENT Content • Physical quantities and SI units • Errors and uncertainties • Scalars and vectors Learning Outcomes Candidates should be able to: (a) recall and use the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol). (b) recall and use the following prefixes and their symbols to indicate decimal sub - multiples or multiples of both base and derived units: pico (p), nano (n), micro (), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T). (c) express derived units as products or quotients of the SI base units and use the named units listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate. (d) use SI base units to check the homogeneity of physical equations. (e) make reasonable estimates of physical quantities included within the syllabus. (f) show an understanding of the distinction between random errors and systematic errors (including zero error) which limit precision and accuracy. (g) assess the uncertainty in derived quantit ies by addi ng absolute or relative (i.e. fractional or percentage) uncertainties or by numerical substitution (rigorous statistical treatment is not required). (h) distinguish between scalar and vector quantities, and give examples of each. (i) add and subtract coplanar vectors. (j) represent a vector as two perpendicular components.

2 Introduction ▪ Physics aims to understand the natural world around us. It encompasses the study of systems spanning a wide range of distances and times: from 10 −15 m (e.g. sub -atomic particles) to larger than 1030 m (e.g. galaxies), from near-instantaneous events, such as the current flow with a flick of a switch, to slow-evolving phenomena, such as the birth and death of a star. Physicists make use of models such as mathematical relationships and graphs to explain and analyse systems. ▪ Scientific experiments are then designed to test the validity of the models. Such experiments involve the measurement of various physical quantities. The precision of any experimental result is reflected in the number of significant figures recorded. ▪ In this topic, you will learn different physical quantities, their SI units and the manipulation of errors and uncertainties incurred when taking measurements. Physical quantities can also be classified as scalars or vectors, and you will learn how to add vectors and resolve them into its components. 1 SI units (a) recall and use the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol). 1.1 Physical quantities ▪ Physical quantities are quantities that can be measured. ▪ A physical quantity consists of a numerical value and a unit. ▪ For example, the height of a man is about 1.70 m. In experiments, instruments are used for the measurement and recording of various physical quantities. Some examples are: physical quantity instrument mass, weight spring balance, lever balance, electronic balance length ruler, vernier callipers, micrometer screw gauge time stopwatch, clock, cathode ray oscilloscope temperature thermometer angle protractor electric current ammeter potential difference voltmeter h = 1.70 m numerical value unit physical quantity

3 ▪ In 1960, the international scientific community adopted a number of conventions about physical quantities and their units. The Système Internationale d’Unités (International System of Units) is based on seven base quantities and their corresponding units, called base units. 1.2 Base quantities and base units ▪ Base quantities are physical quantities that are fundamental and are not defined in terms of other physical quantities. *not in syllabus ▪ There are other physical quantities such as velocity and pressure that need to be measured. Such physical quantities are called derived quantities. (c) express derived units as products or quotients of the SI base units and use the named units listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate. 1.3 Derived quantities and derived units ▪ Derived quantities are physical quantities that are defined in terms of base quantities according to a defining equation. For example, velocity is a d erived qua ntity and it has the defining equation change in displacement time takenv = . ▪ Units of derived quantities are called derived units and are expressed as products or quotients of base units. ▪ Derived units can be obtained from the defining equation as follows: The defining equation for velocity is change in displacement time takenv = . Hence, the unit of velocity is m s–1 (metre per second). [Note the space break between the m and s–1]. base quantity usual symbol for base quantity SI base unit symbol for base unit mass m kilogram kg length l metre m time t second s electric current I ampere A thermodynamic temperature T kelvin K amount of substance n mole mol luminous intensity* L candela cd

4 ▪ In determining derived units, it is important to differentiate between symbols used for the physical quantities and the corresponding symbols for units. A summary of the usual symbols and units for different physical quantities can be found on pages 39 – 40 of the 9748 H2 Physics syllabus document or on pages 23 – 24 of the 8867 H1 Physics syllabus document. (www.seab.gov.sg). derived quantity defining equation derived unit usual unit acceleration t uv −=time velocityinchange 1 2ms mss − −= - force ( ) t uvm −= time momentuminchange 2 1 smkgs smkg − − = newton (N) pressure A F=area force 21 2 2 smkg m smkg −− − = pascal (Pa) work force  displacement in the direction of the force Fs= 22 2 smkg msmkg − − = joule (J) power t E=time work 32 22 smkg s smkg − − = watt (W) potential difference Q E=charge work 132 22 Asmkg sA smkg −− − = volt (V) 1.4 Dimensionless quantities and dimensionless constants ▪ Dimensionless quantities are physical quantities that have no units. Some examples are refractive index and relative molecular mass. ▪ All real numbers and some mathematical constants like  have no units. They are called dimensionless constants. ▪ Note: Some physical quantities that are constants have units. Some examples are: o acceleration of free fall, g = 9.81 m s−2, o elementary charge, −= 191.60 10 Ce

5 (d) use SI base units to check the homogeneity of physical equations. 1.5 Homogeneity of equations ▪ An equation is called homogeneous or dimensionally consistent if every term on both sides of the equation has the same units. That is, units on the LHS = units on the RHS. ▪ For example, for a n equation W = X + Y, the units of the physical quantities W, X and Y must be the same. ▪ Base units can be used to check the homogeneity of physical equations. ▪ An equation that is physically correct must be dimensionally consistent or homogeneous. ▪ However, note that an equation that is dimensionally consistent or homogeneous may NOT be physically correct. Example 1 Determine whether the following equations are homogeneous and state whether they are physically correct. (a) v = u + at (b) v = u + 2at (c) s = ut + at where s is displacement, v is final velocity, u is initial velocity and a is acceleration. Solution: (a) v = u + at Unit of v = m s−1