Physics XI — Chapter 1: Measurement

Vocabulary practice flashcards covering fundamental concepts, SI base and derived units, prefixes, error, uncertainty propagation, significant figures, precision vs. accuracy, and dimensional analysis from Physics Chapter 1: Measurement.

Physics

The branch of science that studies the physical world, including matter, energy, motion, and the relationship between them.

Physical quantity

A quantity that can be measured objectively, such as length, time, mass, temperature, density, and electric current.

System of units

A complete set of units used to measure all physical quantities.

Base unit

A standard unit selected independently for a base physical quantity, such as the metre, kilogram, and second.

Derived unit

A unit obtained by combining base units according to a physical equation, such as $\text{m}\,\text{s}^{-1}$ or $\text{N} = \text{kg}\,\text{m}\,\text{s}^{-2}$.

Radian (rad)

The angle subtended at the centre of a circle by an arc whose length is equal to the radius ($\theta = \frac{s}{r}$).

Steradian (sr)

The solid angle subtended at the centre of a sphere by a surface area equal to the square of the sphere's radius ($\Omega = \frac{A}{r^2}$).

Scientific notation

A method of expressing a number as $a \times 10^n$, where $1 \le a < 10$, $a$ is the mantissa or coefficient, and $n$ is an integer exponent.

Light-year

The distance travelled by light in one year, approximately equal to $9.46 \times 10^{15}\,\text{m}$.

Ångström (Å)

A unit of length defined as $1\,\text{Å} = 10^{-10}\,\text{m}$.

Micron (micrometre)

A unit of length defined as $1\,\mu\text{m} = 10^{-6}\,\text{m}$.

Error

The difference between a measured value and the true value, representing a physical difference in measurement.

Systematic error

An error that tends to have the same sign and direction in repeated measurements, often caused by instrumental flaws, zero errors, calibration issues, or observer bias.

Random error

An error that varies irregularly in sign and magnitude due to unpredictable environmental fluctuations or observer variation, reducible by repeating measurements and averaging.

Least count

The smallest increment or finest resolution that a measuring instrument can detect and read.

Uncertainty

A quantified estimate of the doubt, range, or confidence interval associated with a measured result.

Absolute uncertainty

The magnitude of uncertainty in a measurement, written as $\Delta A$, which carries the same physical unit as the measured quantity.

Relative uncertainty

The dimensionless ratio of the absolute uncertainty to the measured value, expressed as $\frac{\Delta A}{A}$.

Percentage uncertainty

The relative uncertainty of a measurement converted into a percentage: $\frac{\Delta A}{A} \times 100\%$.

Uncertainty propagation for addition and subtraction

The rule stating that when adding or subtracting measured quantities, their absolute uncertainties must be added: $\Delta Z = \Delta A + \Delta B$.

Uncertainty propagation for multiplication and division

The rule stating that when multiplying or dividing measured quantities, their percentage uncertainties must be added: $\%\Delta Z = \%\Delta A + \%\Delta B$.

Uncertainty propagation for powers

The rule stating that when a quantity is raised to a power $n$, its percentage uncertainty is multiplied by $n$: $\%\Delta Z = n(\%\Delta A)$.

Significant figures

All reliably known digits in a measurement plus the first doubtful or estimated digit.

Precision

The closeness of repeated readings of the same quantity to one another, governed by instrument resolution and measuring technique.

Accuracy

The closeness of a measured value or mean of measurements to the accepted or true value, governed by calibration and correctness.

Dimensions of a physical quantity

The qualitative nature of a physical quantity expressed in terms of powers of base quantities, typically written in square brackets such as $[M^a L^b T^c]$.

Dimensional variable

A physical quantity that possesses dimensions and has a changing or variable magnitude, such as force, velocity, or acceleration.

Dimensional constant

A quantity that possesses physical dimensions but maintains a constant numerical value, such as the gravitational constant ($G$) or Planck constant ($h$).

Dimensionless variable

A physical quantity that has no physical dimensions ($[M^0 L^0 T^0]$) but can have varying magnitudes, such as strain, refractive index, or plane angle.

Dimensionless constant

A quantity that has neither dimensions nor variable magnitude, such as pure numbers and $\pi$.

Dimensional equation

An equation that equates a physical quantity to its dimensional formula, such as $[F] = [M L T^{-2}]$.

Principle of dimensional homogeneity

The principle stating that a physical equation is dimensionally consistent only if the dimensions of the terms on the left-hand side equal the dimensions of the terms on the right-hand side.