Units and Measurements

This set of vocabulary flashcards covers fundamental concepts of units, measurement systems, SI base quantities, measurement techniques, error analysis, significant figures, and dimensional analysis based on the provided lecture notes.

Unit

A certain basic, international accepted reference standard used for comparison in the measurement of any physical quantity.

CGS System

A system of units based on the Centimeter, Gram, and Second.

FPS System

A system of units based on the Foot, Pound, and Second.

MKS System

A system of units based on the Meter, Kilogram, and Second.

Radian (rad)

The unit used to measure a plane angle.

Steridian (ST)

The unit used to measure a solid angle.

Vernier callipers

An instrument used for measuring length to an accuracy of $10^{-4}\,m$.

Screwgauge

An instrument used for measuring length to an accuracy of $10^{-5}\,m$.

Basis

The distance between two points of observation in the Parallax method.

Parallax angle ($\theta$)

The angle formed when the distance $D$ is very large and the basis $b$ is taken as an arc length, calculated as $\theta = \frac{b}{D}$.

Unified atomic mass unit (u)

A standard unit of mass for atoms and molecules, equal to $\frac{1}{12}$ the mass of an atom of Carbon-12, or $1.66 \times 10^{-27}\,kg$.

Second

The time duration equal to $9,192,631,770$ vibrations of the radiation corresponding to the transition between hyperfine levels of the ground state of the Cesium atom.

Error

The uncertainty inherent in a measurement.

Accuracy

A measure of how close a measured value is to the true value of the quantity.

Precision

The closeness of two or more measurements to each other, which depends on the resolution of the instrument.

Systematic errors

Errors that arise due to faulty instruments (instrumental errors), imperfections in experimental technique, or personal bias and carelessness.

Zero error

A specific instrumental error where the zero mark of a scale (such as a vernier scale) does not coincide with the zero mark on the main scale.

Random errors

Errors that arise due to random and unpredictable fluctuations in experimental conditions.

Least count error

The error associated with the smallest value that can be measured by a measuring instrument, related to its resolution.

Absolute error

The magnitude of the difference between an individual measurement and the true value (or mean value) of the quantity, always expressed as a positive value.

Relative error

The ratio of the mean absolute error ($\Delta a_{mean}$) to the mean value ($a_{mean}$) of the quantity measured.

Percentage error

The relative error expressed as a percentage, calculated as $Relative\,error \times 100$.

Significant figures

The reliable digits in a measurement plus the first uncertain digit.

Dimensions

The powers to which base quantities are raised to represent a specific physical quantity, usually denoted with brackets $[ ]$.

Principle of Homogeneity

The principle stating that physical quantities can only be added or subtracted if they have the same dimensions.