Physics: Measurement and Units Overview

Study Notes

Physical quantities are described by both magnitude and units.
Units of measurement are standardized magnitudes used for comparisons.
Measurement involves determining the magnitude of a physical quantity using an instrument.
Fundamental units are basic units like meters, kilograms, and seconds.
Derived units are combinations of fundamental units.
Dimensions represent the physical nature of a quantity.
Dimensional analysis relates quantities and their dimensions using equations.

Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.
SI prefixes are used to express very large or very small quantities.

Measurements have associated uncertainties due to limitations of instruments and techniques.
Uncertainty represents the range of probable values for the true value.
Measurements are expressed in the format: (best estimate ± uncertainty) unit.
Sources of error include instruments, procedures, and the measured quantity itself.
Types of errors include systematic and random errors.
Systematic errors consistently bias readings in one direction.
Random errors cause unpredictable variations in readings.
Averaging multiple measurements reduces the effect of random errors.
Significant figures reflect the precision of a measurement.
The product or ratio of measurements has the same number of significant figures as the measurement with the fewest significant figures.

Order of magnitude expresses the approximate size of a quantity as a power of 10.
It's useful for estimations and comparisons, particularly when accuracy is less critical.

Vectors have both magnitude and direction.
Examples include force, velocity, and acceleration.
Vectors can be added/subtracted graphically using the triangle or parallelogram method.
Vectors are added component-wise.
Components are scalar quantities representing vector projections along coordinate axes.
The magnitude of a vector is calculated by the Pythagorean theorem applied to its components.
The direction of a vector can be determined from its components.
Vector equality requires both magnitude and direction to be identical when comparing with another vector.