Learning Objectives
- Understand the seven base units of the International System of Units (SI) and their precise definitions based on fundamental constants.
- Apply dimensional analysis to check the consistency of equations, derive relations among physical quantities, and understand the dimensions of derived units.
- Determine significant figures in measurements and calculations, including rounding off and maintaining precision in arithmetic operations.
- Derive dimensional formulae for various physical quantities and use dimensional equations to represent these relationships.
- Understand derived units in terms of base units and their application in expressing physical quantities, including special names for some derived units.
- Use scientific notation and order of magnitude to express and compare large and small quantities, emphasizing the precision and scale of measurements.
- Ensure equations are dimensionally consistent, which is a necessary condition for their correctness, though not sufficient for physical accuracy.
- Convert between different unit systems such as CGS, FPS, MKS, and SI, and perform unit conversions like cm–m, km/h–m/s, joule–erg, density units, and new unit systems.
- Apply rules for multiplication/division and addition/subtraction using significant figures and decimal-place precision.
- Analyze measurement uncertainty and error propagation, including absolute error, relative/percentage error, uncertainty in arithmetic operations, and reliability of repeated measurements.
- Differentiate between accuracy and precision, understand the least count of instruments, and compare measuring devices like vernier calipers and screw gauge.