Overview
This lecture covers the foundational Plus One Physics chapter "Units and Measurements," focusing on SI units, dimensional analysis, significant figures, and key exam concepts and definitions.
SI Fundamental Quantities and Units
- There are seven SI fundamental quantities: Length (meter-m), Mass (kilogram-kg), Time (second-s), Electric current (ampere-A), Temperature (kelvin-K), Amount of substance (mole-mol), and Luminous intensity (candela-cd).
- Each quantity has its symbol and SI unit, which must be memorized for the exam.
Supplementary Quantities: Plane and Solid Angle
- Plane angle is the ratio of arc length to the radius (unit: radian, symbol: rad; dimensionless).
- Solid angle is the ratio of intercepted area to the square of the radius (unit: steradian, symbol: sr; dimensionless).
Significant Figures
- For decimals, all digits from the first non-zero to the end are significant.
- For non-decimals, only digits between the first and last non-zero are significant.
- Exact numbers (like 5 apples) have infinite significant figures.
- Powers or exponents do not affect significant figures; only the coefficient counts.
Dimensional Analysis Basics
- Each physical quantity can be expressed in terms of fundamental dimensions: Length [L], Mass [M], Time [T], Current [I], Temperature [K], Amount of substance [mol], Luminous Intensity [cd].
- Examples:
- Speed: [L][T^-1]; Acceleration: [L][T^-2]
- Force: [M][L][T^-2]; Work/Energy: [M][L^2][T^-2]
- Area: [L^2]; Volume: [L^3]; Density: [M][L^-3]
Principle of Homogeneity
- Only quantities with the same dimensional formula can be added or subtracted.
- Dimensional analysis can verify whether equations are dimensionally correct but not whether they are actually correct physically.
Dimensional Analysis for Deriving Formulas
- To derive relations, equate the dimensions on both sides and solve for powers.
- Examples shown: Kinetic energy (dependent on mass and velocity), Period of simple pendulum (dependent on length and gravity), Centripetal force (dependent on mass, velocity, and radius).
Limitations of Dimensional Analysis
- Cannot determine the value of dimensionless constants in equations.
- Cannot verify the correctness of an equation, only dimensional consistency.
- Cannot analyze equations involving trigonometric, exponential, or logarithmic terms.
Key Terms & Definitions
- SI Units — Standard international units for measurement used globally.
- Plane Angle — Ratio of arc length to radius (radian).
- Solid Angle — Ratio of intercepted area to radius squared (steradian).
- Significant Figures — Digits in a measurement that carry meaning for precision.
- Dimensional Formula — Representation using fundamental dimensions.
- Principle of Homogeneity — Only same-dimensional quantities can be added/subtracted.
Action Items / Next Steps
- Memorize all SI fundamental and supplementary units, their symbols, and dimensions.
- Practice previous year questions on Units and Measurements.
- Review and master rules for significant figures and dimensional analysis.
- Skip "Range of Length," "Errors," and "Parallax Method" (deleted topics for this exam).
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