TLDR;
This lecture provides a comprehensive overview of units and measurement in physics, covering fundamental and derived units, dimensional analysis, and error measurement. It explains the importance of understanding these concepts for a solid foundation in physics.
- Introduces the system of units, including CGS, MKS, FPS, and SI units.
- Explains fundamental and derived units with examples.
- Discusses dimensions and dimensional analysis, including how to calculate dimensions for physical quantities.
- Covers errors in measurement, including systematic and random errors, and how to estimate them.
Introduction [0:00]
The lecture begins by emphasising the importance of understanding the concepts in physics, particularly units and measurement, for building a strong foundation. Physics is presented not as a difficult subject, but one that requires conceptual clarity and the ability to express understanding in English. The lecture aims to cover key topics such as the system of units, fundamental and supplementary units, dimensional analysis, errors in measurement, and significant figures.
System of Units [11:42]
The discussion moves to the system of units, explaining that units are used to measure physical quantities. Different systems exist, including CGS (centimetre, gram, second), MKS (metre, kilogram, second), FPS (foot, pound, second), and SI (System International) units. The SI system is a more recent development and includes seven fundamental units, unlike the MKS system, which only has three.
Fundamental Units [12:11]
Physical quantities are classified into fundamental and derived quantities. Fundamental quantities are those that do not depend on other physical quantities for their measurement. There are seven fundamental quantities: length, mass, time, temperature, electric current, luminous intensity, and amount of substance. Each has a corresponding SI unit: metre (m), kilogram (kg), second (s), Kelvin (K), Ampere (A), Candela (cd), and mole (mol).
Derived Units [16:51]
Derived units are those that can be expressed in terms of fundamental units. Examples include speed, velocity, and acceleration. To measure velocity, displacement and time must be measured. The units for these derived quantities are combinations of fundamental units, such as kilometres per hour or metres per second squared.
Plane Angle [18:31]
Supplementary units include plane angle and solid angle. A plane angle, denoted as theta, is measured in radians (rad) and is defined as the ratio of the arc length to the radius of a circle (θ = arc/radius). Plane angle is a dimensionless quantity because it is a ratio of two lengths, and its unit is the radian.
Solid Angle [22:04]
A solid angle is the three-dimensional analogue of a plane angle and is measured in steradians. It is defined as the area of a portion of the surface of a sphere divided by the square of the radius of the sphere. Like the plane angle, the solid angle is also a dimensionless quantity.
Conventions for the Use of SI Units [24:15]
Several conventions should be followed when using SI units:
- Units should be represented by their symbols (e.g., m for metre, A for Ampere).
- Full names of units start with a small letter, but symbols for units named after a person are capitalised (e.g., Ampere is A, Kelvin is K).
- Symbols do not take plural forms (e.g., 10 kg, not 10 kgs).
- No full stop is used after symbols.
- Ratios should be written as metre per second squared (m/s²), not metre per second per second.
- Combinations of units and symbols should be avoided.
- Prefixes should be used before the unit symbol, avoiding double prefixes.
- A space or hyphen should be used to indicate multiplication of two units (e.g., kg metre per second).
Dimension and Dimensional Analysis [37:36]
Dimensions refer to the fundamental units that constitute a physical quantity. The dimension of a physical quantity is the power to which the fundamental units must be raised to obtain the unit of that quantity. For example, the dimension of force is mass × acceleration, which is kg × m/s². In terms of dimensions, force is represented as [M¹L¹T⁻²]. Dimensional analysis is used to check the correctness of physical equations, establish relations between physical quantities, and find conversion factors between units.
Errors in Measurement [49:05]
Errors in measurement are inevitable. Accuracy refers to how close a measurement is to the actual value, while precision refers to the consistency of repeated measurements. Uncertainties arise due to various factors, including instrument limitations and environmental conditions. Errors are classified as systematic (instrumental, imperfect technique, personal) and random. Absolute error is the difference between the mean value and each individual value. The mean absolute error is the average of all absolute errors. Relative error is the ratio of the mean absolute error to the average value, and percentage error is the relative error expressed as a percentage.