Physics: Measurement of Physical Quantities and Representation of Data

Vocabulary practice flashcards covering introductory physics: the scientific method, the International System of Units (SI), length, area, volume, mass, time, density, scientific notation, experimental errors, significant figures, and mathematical representations of physical phenomena (tables, Cartesian graphs, slopes, direct/inverse/quadratic proportionalities, linear correlation, and periodic functions).

Natural Philosophy

The historical branch of philosophy dedicated to observing natural phenomena, encompassing modern physics, chemistry, and biology until the 19th century, studied by thinkers such as Parmenides, Pythagoras, and Aristotle.

Experimental Method

The scientific method formulated by Galileo Galilei (1564–1642), stating that natural laws must be investigated through experiments and empirical verification rather than deduced from sacred texts or classical authorities.

Four Stages of the Experimental Method

The sequential phases of scientific investigation: 1. Observation of the phenomenon; 2. Formulation of a hypothesis; 3. Experimental verification of the hypothesis; 4. Drawing conclusions (the hypothesis becomes a law if confirmed, or is discarded if rejected).

Physical Quantity

Any objective, measurable characteristic of a body or phenomenon (such as length or mass) for which a unit of measurement can be established, unlike subjective qualities such as friendliness or romance.

Measurement

The operation of choosing a unit of measurement, comparing it to the quantity to be measured, and counting how many times that unit is contained within the unknown quantity.

International System of Units (SI)

The globally adopted measurement system that definitively came into force in $1978$, evolved from the late-18th-century French decimal metric system, defining standard units for seven fundamental quantities.

Base Quantities (SI)

The seven independent physical quantities defined by the SI: length (metre, $\text{m}$), mass (kilogram, $\text{kg}$), time (second, $\text{s}$), temperature (kelvin, $\text{K}$), electric current (ampere, $\text{A}$), luminous intensity (candela, $\text{cd}$), and amount of substance (mole, $\text{mol}$).

Derived Quantities

Physical quantities obtained from mathematical combinations (multiplication or division) of base physical quantities, such as speed ($\text{m/s}$), area ($\text{m}^2$), and volume ($\text{m}^3$).

Homogeneous Physical Quantities

Physical quantities of the exact same kind (e.g., two lengths or two masses) that can be compared, added, or subtracted directly.

Metre

The SI base unit of length ($\text{m}$), originally defined as $1/40\,000\,000$ of the Earth's meridian and represented by a platinum-iridium bar at Sèvres until $1960$; since $1983$, it is defined as the distance traveled by light in a vacuum in $1/299\,792\,458\,\text{s}$.

Kilogram

The SI base unit of mass ($\text{kg}$), historically defined by a prototype cylinder of platinum-iridium kept at Sèvres until $2019$, when it was redefined in terms of the fundamental Planck constant.

Second

The SI base unit of time ($\text{s}$), historically based on pendulum oscillations or astronomical movements, and defined since $1967$ by specific properties of the caesium atom.

Micrometre (Micron)

A submultiple of the metre with symbol $\mu\text{m}$, equal to one-millionth of a metre ($1\,\mu\text{m} = 0.000\,001\,\text{m} = 10^{-6}\,\text{m}$), commonly used to measure microscopic entities like bacteria.

Light-Year

A non-SI astronomical unit of distance equal to the path traveled by light in one year, corresponding to $9\,460\,000\,000\,000\,000\,\text{m}$ (approximately $10^{13}\,\text{km}$).

Square Metre

The derived SI unit of area with symbol $\text{m}^2$, representing the area of a square with sides of length $1\,\text{m}$, equivalent to $10\,000\,\text{cm}^2$.

Hectare

A non-SI unit of surface area with symbol $\text{ha}$, commonly used in land measurement, equal to $10\,000\,\text{m}^2$ or the area of a square with a side length of $100\,\text{m}$.

Cubic Metre

The derived SI unit of volume with symbol $\text{m}^3$, defined as the space occupied by a cube with edges of length $1\,\text{m}$, equivalent to $1\,000\,000\,\text{cm}^3$ or $1000\,\text{dm}^3$.

Litre

A common unit of volume with symbol $\text{L}$, defined as equal to one cubic decimetre ($1\,\text{L} = 1\,\text{dm}^3$), such that $1\,\text{m}^3 = 1000\,\text{L}$.

Liquid Displacement Method

A laboratory technique used to find the volume of an irregularly shaped solid by immersing it in a graduated cylinder filled with liquid and calculating the difference between the final volume ($V_f$) and initial volume ($V_i$): $V = V_f - V_i$.

Mass

An intrinsic, constant property of an object expressing the quantity of matter it contains and its inertia, measured in kilograms ($\text{kg}$) in the SI.

Inertia

The inherent physical tendency of an object to resist changes to its state of rest or motion.

Equal-Arm Balance

An instrument designed to measure mass by balancing a rigid horizontal beam pivoted at its center, directly comparing an unknown mass on one pan against calibrated reference masses on the other.

Weight

The gravitational force with which a celestial body (such as the Earth) attracts an object towards its center, varying according to distance from the center and the planetary body.

Law of Conservation of Mass

A foundational chemical principle established by Antoine-Laurent de Lavoisier (1743–1794), stating that the total mass of substances remains constant during physical mixing and chemical reactions.

Density

A characteristic physical property of a homogeneous substance defined as the ratio of its mass to the volume it occupies: $d = \frac{m}{V}$, expressed in $\text{kg/m}^3$ in the SI.

Density Conversion Factor

The conversion rule between density units where $1\,\text{g/cm}^3 = 1000\,\text{kg/m}^3$; converting a value from $\text{kg/m}^3$ to $\text{g/cm}^3$ requires dividing by $1000$.

Osmium

The densest naturally occurring solid substance listed in the text, having a density of $22\,500\,\text{kg/m}^3$.

Radon

The densest gas listed in the text, having a density of $9.73\,\text{kg/m}^3$ at $0\,^\circ\text{C}$ and $1\,\text{atm}$.

Scientific Notation

A standard format for writing very large or very small numbers as a product $b = a \times 10^n$, where $1 \le a < 10$ and $n$ is a positive or negative integer.

Order of Magnitude

The power of $10$ closest to the numerical value of a quantity, used for rapid comparisons and checking the reasonableness of calculations.

Random Errors

Unpredictable fluctuations occurring during measurement that can randomly lead to results that are higher or lower than the true value.

Systematic Errors

Errors that repeat consistently in the same direction—always in excess or always in deficit—such as those caused by an expanded or incorrectly calibrated measuring instrument.

Instrument Sensitivity

The smallest change or increment in a physical quantity that a measuring instrument can detect and indicate.

Absolute Error

The estimated uncertainty associated with a measured quantity, written as $x \pm e_a$, having the same unit of measurement as the quantity itself.

Mean Value

The central estimate calculated from repeated measurements of the same quantity, defined as the sum of all measurements divided by the total number of measurements.

Absolute Error of Multiple Measurements

The uncertainty calculated from a set of repeated measurements, defined as half the difference between the maximum and minimum measured values: $e_a = \frac{\text{maximum value} - \text{minimum value}}{2}$.

Relative Error

The dimensionless ratio of the absolute error to the mean value of a measurement: $e_r = \frac{e_a}{\bar{x}}$.

Percentage Error

The relative error expressed as a percentage, calculated by multiplying the relative error by $100\%$: $e_p = (e_r \times 100)\%$.

Indirect Measurement

A measurement where the value of a target quantity is obtained through mathematical operations performed on other directly measured quantities (e.g., calculating density from mass and volume).

Error Propagation in Sums and Differences

The rule establishing that when a quantity is determined by adding or subtracting measured quantities ($G = A + B$ or $G = A - B$), the absolute error of the result is the sum of the individual absolute errors: $e_a(G) = e_a(A) + e_a(B)$.

Error Propagation in Products and Quotients

The rule establishing that when a quantity is determined by multiplying or dividing measured quantities ($G = A \cdot B$ or $G = \frac{A}{B}$), the relative error of the result is the sum of the individual relative errors: $e_r(G) = e_r(A) + e_r(B)$.

Significant Figures

All the certain digits of a measured quantity plus the first uncertain digit, where leading zeros are never significant, but trailing zeros to the right of the decimal point are significant.

Independent Variable

The known input variable in an experiment or mathematical model (typically plotted on the horizontal $x$-axis, such as time) that changes independently.

Dependent Variable

The variable whose value depends on and changes in response to the independent variable, typically represented on the vertical $y$-axis.

Physical Law

A mathematical relationship (function) describing a natural phenomenon based on experimental results that allows predictions of future or unobserved states.

Cartesian Graph

A two-dimensional coordinate diagram displaying the functional relationship between an independent variable on the horizontal axis (abscissa) and a dependent variable on the vertical axis (ordinate).

Graphical Interpolation

The process of estimating an unmeasured intermediate value between known data points on a graph using a drawn curve or line.

Slope of a Straight Line

The constant ratio between the change in the vertical coordinate and the change in the horizontal coordinate between any two points on a line: $p = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$.

Delta ($\Delta$)

The Greek letter used in physics and mathematics to designate the variation, difference, or increment in a quantity between two states ($\Delta x = x_2 - x_1$).

Direct Proportionality

The mathematical relationship between two variables $x$ and $y$ where their ratio remains constant: $\frac{y}{x} = k$ (or $y = k \cdot x$), producing a straight-line graph passing through the origin $(0,0)$.

Constant of Proportionality ($k$)

The fixed non-zero ratio $k$ between two directly proportional quantities, representing the slope of the resulting linear graph through the origin.

Linear Correlation

The relationship between two variables described by $y = k \cdot x + c$, where variations relative to an initial offset $c$ are directly proportional, represented graphically by a straight line that does not pass through the origin.

Quadratic Proportionality

The mathematical relationship where a variable $y$ is directly proportional to the square of variable $x$, expressed as $y = k \cdot x^2$, producing a parabolic curve on a Cartesian graph.

Parabola

The characteristic curved graph representing a quadratic proportionality relationship ($y = k \cdot x^2$), such as the relationship between a circle's area and its radius ($A = \pi \cdot r^2$).

Inverse Proportionality

The mathematical relationship between two variables whose product is constant: $x \cdot y = k$ (or $y = \frac{k}{x}$), such that doubling one variable halves the other.

Hyperbola

The characteristic curved graph representing an inverse proportionality relationship ($y = \frac{k}{x}$), exemplified by the distance and balancing mass on a lever ($d \cdot m = \text{constant}$).

Periodic Motion

A repetitive physical motion where an object returns to the exact same position and kinematic state at regular, fixed time intervals.

Period ($T$)

The duration of time required for an object undergoing periodic motion to complete one full cycle (such as $T = 2\,\text{s}$ for a complete back-and-forth oscillation of a pendulum).