Physics Chapter 1: Measurements

Study Notes

Chapter 1: Measurements

Learning Objectives: Students will be able to understand what Physics is, recall base quantities and their units (mass, length, time, current, temperature, luminous intensity, and amount of substance), describe and use base units, supplementary units, and derived units, understand and use scientific notation, use standard prefixes, understand conventions for indicating units, distinguish between systematic and random errors, understand significant figures, assess uncertainty, quote answers with correct notation and units, use dimensionality, and derive formulae.
Introduction to Physics: Physics is a fundamental science concerned with the study of matter and energy, and their relationships. It encompasses extremely large (the universe) and extremely small (particles) scales, and focuses on the "middle-sized" world between these extremes.
Physical Quantities: The foundation of physics rests upon physical quantities that describe the physical world. These are categorized as base quantities (like length, mass, time), and derived quantities (like velocity, force, density, etc.). Derived quantities are built from base quantities.
International System of Units (SI): A standardized system used globally for describing physical quantities. It includes seven base units (meter, kilogram, second, ampere, kelvin, candela, and mole) and supplementary units (radian and steradian). Derived units are combinations of base or supplementary units.
Significant Figures: Represent the degree of accuracy in a measurement. Rules for determining the number of significant figures are necessary for calculations involving measured values. Rules include that all non-zero digits are significant, zeros between significant figures are significant, and zeros to the right of the decimal point in a number are significant. Zeros to the left of the first non-zero digit are not considered significant.
Measurement Errors: All physical measurements have some degree of uncertainty or error. Errors can be either random (due to uncontrolled or unknown factors) or systematic (due to a flaw in the instrument/method; consistent in direction and magnitude). Errors in measurements affect precision, which refers to how close repeated measurements are to each other, and accuracy, which refers to how close the measurements are to the true value.
Uncertainty in Measurements: Uncertainty in measurements must be considered, especially when performing calculations. Precise instruments provide smaller uncertainties. Errors can lead to uncertainty when using multiple measurements. Uncertainty values are related to the least count or smallest graduation of the measuring instrument. Absolute uncertainty is often expressed as plus/minus a value. For example, "10±1 cm" or "10.0 cm (accurate to 1 mm)", which in most situations would be better written as "10 ±0.1 cm." Calculating uncertainty in the results of a calculation involves carefully considering whether calculations involve multiplication, division, addition, or subtraction. Rules and procedures are applied to calculate the final uncertainty in the result.
Dimensional analysis: A method used to check the homogeneity of physical equations. It involves analyzing the dimensions of quantities in a formula to ensure that the equation is correct. This principle demonstrates consistency of equation dimensions.
Questions and Examples: Exercises and problems are covered demonstrating how to apply the concepts and principles discussed. These examples are often included for practice to ensure thorough understanding.