Units, Measurement, and Vectors – Key Vocabulary

Vocabulary flashcards covering essential terms from the lecture on SI units, measurement principles, errors, uncertainties, and vector operations.

Physical Quantity

A measurable property of a physical system expressed by a number and a unit (e.g., mass, time).

Fundamental Quantity

A basic physical quantity that exists independently (time, length, mass, etc.).

Derived Quantity

A quantity defined by combinations of fundamental quantities (e.g., speed, density).

Scalar Quantity

A quantity described only by magnitude (e.g., energy, distance).

Vector Quantity

A quantity described by both magnitude and direction (e.g., velocity, force).

SI (Système Internationale)

Internationally accepted system of units used in science.

Second (s)

SI base unit of time.

Meter (m)

SI base unit of length.

Kilogram (kg)

SI base unit of mass.

Ampere (A)

SI base unit of electric current.

Kelvin (K)

SI base unit of thermodynamic temperature.

Mole (mol)

SI base unit of amount of substance.

Candela (cd)

SI base unit of luminous intensity.

Yotta (Y)

SI prefix for 10²⁴.

Zetta (Z)

SI prefix for 10²¹.

Exa (E)

SI prefix for 10¹⁸.

Peta (P)

SI prefix for 10¹⁵.

Tera (T)

SI prefix for 10¹².

Giga (G)

SI prefix for 10⁹.

Mega (M)

SI prefix for 10⁶.

Kilo (k)

SI prefix for 10³.

Milli (m)

SI prefix for 10⁻³.

Micro (µ)

SI prefix for 10⁻⁶.

Nano (n)

SI prefix for 10⁻⁹.

Pico (p)

SI prefix for 10⁻¹².

Femto (f)

SI prefix for 10⁻¹⁵.

Atto (a)

SI prefix for 10⁻¹⁸.

Zepto (z)

SI prefix for 10⁻²¹.

Yocto (y)

SI prefix for 10⁻²⁴.

Unit Conversion

Process of changing measurements to equivalent values in different units.

Straightforward Linear Conversion

Single-step unit change using a direct equality (e.g., 1 mi = 1609 m).

Chain Conversion

Sequential application of multiple conversion factors (e.g., mi/h → m/s).

Power Conversion

Unit change involving squared or cubed units (e.g., m² → cm²).

Measurement

Process of comparing an unknown quantity with a standard and assigning a numerical value with units.

Precision

Degree of fineness or repeatability in measurements.

Accuracy

Closeness of a measurement to the true or standard value.

Percent Error

|measured − standard| / standard × 100 %; quantifies accuracy.

Systematic Error

Consistent deviation due to instrument calibration or environmental effects.

Random Error

Unpredictable variation arising from measurement limitations.

Least Count (LC)

Smallest division an instrument can reliably measure.

Significant Figures

Digits in a number that convey measured precision, including the estimated last digit.

Uncertainty

Numerical interval expressing doubt in a measurement (e.g., 5.0 ± 0.1 g).

Best Estimate

Central measured value reported with its uncertainty.

Propagation of Uncertainty

Method of combining individual uncertainties to find the uncertainty in a derived quantity.

Unit Vector

A vector of magnitude 1 that indicates direction.

Vector Component

Projection of a vector along an axis (Ax or Ay).

Magnitude

Size or length of a vector, independent of direction.

Direction

Orientation of a vector, often given by an angle or compass bearing.

Resultant Vector

Vector sum of two or more vectors.

Parallelogram Method

Graphical technique for adding two vectors by completing a parallelogram.

Polygon Method

Graphical addition of multiple vectors tip-to-tail to find the resultant.

Law of Cosine

Analytical formula R² = A² + B² − 2AB cos θ for two-vector addition.

Law of Sine

Relation sin α/A = sin β/B = sin γ/C used to solve vector triangles.

Component Method

Analytical addition using algebraic sums of x- and y-components.

Pythagorean Theorem (in vectors)

|R| = √(Rx² + Ry²) to compute vector magnitude from components.

Tangent Function (tan θ)

Ratio Ry/Rx used to determine a vector’s direction angle.

Graphical Scale

Chosen ratio (e.g., 1 cm = 1 m) that links drawing length to vector magnitude.

Chain Rule for Angles

Sign analysis of Rx and Ry to label direction (N of E, S of W, etc.).

Density

Derived quantity equal to mass per unit volume (kg/m³ or g/cm³).