Physics: Measurements, Units, Dimensions, and Errors

Comprehensive vocabulary flashcards covering introductory physics concepts, systems of units (FPS, CGS, MKS, SI), base and derived quantities, dimensional analysis, and measurement errors.

Unit

A fixed, internationally agreed reference magnitude used to express and compare a physical quantity.

Scalar Quantity

A physical quantity that requires only a magnitude and a unit to be fully described (such as mass, time, or temperature).

Vector Quantity

A physical quantity that requires a magnitude, a unit, and a direction, combining according to vector laws (such as the triangle and parallelogram laws) rather than by simple addition.

FPS System

A British / imperial system of units that measures length in feet ($\text{ft}$), mass in pounds ($\text{lb}$), and time in seconds ($\text{s}$).

CGS System

A smaller-scale metric system common in classical physics and chemistry that measures length in centimetres ($\text{cm}$), mass in grams ($\text{g}$), and time in seconds ($\text{s}$).

MKS System

A metric system of units measuring length in metres ($\text{m}$), mass in kilograms ($\text{kg}$), and time in seconds ($\text{s}$), serving as the mechanical foundation of the SI.

Radian

The SI supplementary unit of plane angle, defined as the angle subtended at the centre of a circle by an arc whose length equals the circle's radius ($\theta = \frac{s}{r}$), where $2\pi\text{ radians} = 360^\circ$ ($1\text{ radian} \approx 57.3^\circ$).

Steradian

The SI supplementary unit of solid angle, defined as the solid angle subtended at the centre of a sphere by a surface patch whose area equals the square of the sphere's radius ($\Omega = \frac{A}{r^2}$), where a complete sphere covers $4\pi\text{ steradians}$ ($\approx 12.57\text{ sr}$).

Base Quantities

The minimal set of seven independent physical quantities that are not defined in terms of any other quantity: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

Derived Quantities

Physical quantities formed by combining base quantities through multiplication and/or division (such as speed, force, energy, and pressure).

Dimensions

The representation of a physical quantity that shows which base quantities it is built from and to what power, written in square brackets independent of the specific unit or system used (e.g., speed is always $[\text{L T}^{-1}]$).

Dimensional Homogeneity

The principle stating that a physical equation can only be correct if both sides (and every term added or subtracted) have identical dimensions.

Error

The difference between the measured value and the true (actual) value of a physical quantity.

Error Range

The algebraic difference calculated as $\text{Error Range} = \text{Measured Quantity} - \text{Actual Quantity}$.

Percentage Error

The relative error expressed as a percentage: $\text{\% Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{\text{Actual Value}} \times 100\%$.

Accuracy

A measure of how close a measurement is to the true (actual) value of the quantity, which is lowered primarily by systematic error.

Precision

A measure of how close repeated measurements of the same quantity are to each other, which is lowered primarily by random error.

Systematic Error

Errors caused by a flaw in the instrument or method that shift every reading by roughly the same amount in the same direction, resulting in tightly clustered readings that are consistently off-centre and cannot be removed by averaging.

Random Error

Unpredictable fluctuations that scatter readings above and below the true value with no fixed pattern, which can be reduced by repeating measurements and calculating the mean.

Zero Error

A type of systematic error where an instrument does not read zero when it should (such as an uncalibrated scale indicating $2\,\text{g}$ with nothing on it).

Gross Error

A large mistake resulting from human carelessness, such as misreading a scale, recording an incorrect value, or making an arithmetic slip, which is avoided through care rather than statistical methods.

Least Count

The smallest measurement value that an instrument can reliably distinguish, determined by its smallest scale division (for example, $1\,\text{mm}$ for a standard metre rule).