Physik für Life-Science-Ingenieure 1 - Fundamentals and Mechanics

Vocabulary flashcards covering SI base units, measurement standards, error calculation, statistics, dimensional analysis, and 1D/3D kinematics from the Physics for Life Science Engineers 1 course.

Physical Quantity (Physikalische Größe)

A measurable property of a physical system defined as the product of a numerical value and a physical unit: $G = \{G\} \times [G]$.

Measurement (Messung)

The objective, numerical quantification of a physical property or process expressed as a multiple of an established reference unit value.

Second ($\text{s}$)

The SI base unit of time, defined by setting the fixed numerical value of the Caesium-133 hyperfine transition frequency $\Delta\nu_{\text{Cs}}$ to $9\,192\,631\,770\,\text{Hz}$.

Meter ($\text{m}$)

The SI base unit of length, defined by taking the fixed numerical value of the speed of light in vacuum $c$ to be $299\,792\,458\,\text{m/s}$.

Kilogram ($\text{kg}$)

The SI base unit of mass, defined by setting the Planck constant $h$ to exactly $6.626\,070\,15 \times 10^{-34}\,\text{J\,s}$.

Ampere ($\text{A}$)

The SI base unit of electric current, defined by fixing the elementary charge $e$ to $1.602\,176\,634 \times 10^{-19}\,\text{C}$.

Kelvin ($\text{K}$)

The SI base unit of thermodynamic temperature, defined by setting the Boltzmann constant $k_{\text{B}}$ to $1.380\,649 \times 10^{-23}\,\text{J/K}$.

Mole ($\text{mol}$)

The SI base unit for amount of substance, containing exactly $6.022\,140\,76 \times 10^{23}$ elementary entities, as defined by the Avogadro constant $N_{\text{A}}$.

Candela ($\text{cd}$)

The SI base unit of luminous intensity, defined as the luminous intensity of monochromatic radiation of frequency corresponding to $555\,\text{nm}$ with a radiant intensity of $1.46\,\text{mW}$ per steradian.

Dimensional Analysis (Dimensionsanalyse)

A verification method based on the requirement that all summands and both sides of a physical equation must possess the exact same physical dimension.

Systematic Error (Systematischer Messfehler)

A reproducible error that shifts measurements consistently in the same direction and magnitude, caused by faulty calibration, instrument defects, or personal observer biases.

Statistical Error (Statistischer Messfehler)

An unavoidable, random deviation in positive or negative directions caused by instrument precision limits or natural fluctuations, which can be minimized by repeating measurements.

Arithmetic Mean ($\bar{x}$)

The best estimate of the true value obtained from a series of $n$ independent measurements: $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$.

Standard Deviation of a Single Measurement ($s$)

A statistical quantity describing the dispersion or mean error of individual measured values around the mean: $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (\bar{x} - x_i)^2}$.

Standard Error of the Mean ($\Delta\bar{x}$)

The statistical uncertainty of the calculated arithmetic mean, which decreases with the square root of the number of measurements: $\Delta\bar{x} = \frac{s}{\sqrt{n}}$.

Significant Figures (Signifikante Stellen)

All reliably known digits in a reported measurement that indicate the precision and level of uncertainty of the measured value.

Normal Distribution (Gauß-Verteilung)

A symmetric continuous bell curve describing purely statistical errors, where $68.27\%$ of values lie within $\pm 1\sigma$, $95.45\%$ within $\pm 2\sigma$, and $99.73\%$ within $\pm 3\sigma$ of the mean.

Displacement (Verschiebung)

The directional vector change in position between two points in time: $\Delta x = x(t_2) - x(t_1)$, which is generally distinct from total distance traveled.

Average Velocity (Mittlere Geschwindigkeit)

The quotient of the displacement $\Delta x$ and the elapsed time interval $\Delta t$: $\bar{v} = \frac{\Delta x}{\Delta t}$.

Instantaneous Velocity ($v(t)$)

The time derivative of the position function representing the instantaneous rate of change of position: $v(t) = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt} = \dot{x}$.

Acceleration ($a(t)$)

The rate of change of velocity per unit time, mathematically defined as the first time derivative of velocity and the second time derivative of position: $a(t) = \frac{dv}{dt} = \frac{d^2x}{dt^2} = \ddot{x}$.

Scalar (Skalar)

A physical quantity that is fully characterized by magnitude alone without any direction in space (e.g., mass).

Vector (Vektor)

A physical quantity that has both a magnitude and a spatial direction defined within a chosen coordinate system (e.g., displacement, velocity, force).