Units, Measurements, and Dimensional Analysis

These vocabulary flashcards cover fundamental SI units, dimensional analysis, error propagation, and precision measurement instruments based on the lecture notes.

Fundamental Quantities

The seven basic physical quantities in the updated MKS system: Mass ($kg$), Length ($m$), Time ($s$), Electric current ($Ampere$), Temperature ($Kelvin$), Luminous Intensity ($candela$), and Amount of Substance ($Mole$).

Plane Angle ($\theta$)

A supplementary quantity with the unit Radian, defined by the formula $\theta = \frac{\text{Arc}}{\text{Radius}}$. It has units but is dimensionless.

Solid Angle ($\Omega$)

A supplementary quantity with the unit Steradian, defined by the formula $\frac{\text{Area}}{\text{Radius}^2}$. It has units but is dimensionless.

Dimensionless Quantities

Physical quantities that do not have dimensions, including Relative density, specific gravity, refractive index, coefficient of friction ($\text{μ}$), strain, Relative permittivity ($\text{ε}_r$), and dielectric constant.

Dimensional Analysis Limitations

The method cannot derive formulas depending on more than 3 physical quantities, composite terms, or equations containing exponential, trigonometric, and logarithmic functions.

Accuracy

Refers to how close a measured value is to the true value (e.g., if the true value is $5.00$, $4.95$ is more accurate than $4.70$).

Precision

Refers to the closeness of repeated measurements to each other or the 'bareek value' (fineness) of the measurement, regardless of accuracy.

Absolute Error ($\Delta a$)

The difference between the true value and the measured value, calculated as $\text{True Value} - \text{Measured Value}$.

Relative Error (Fractional Error)

The ratio of the mean absolute error to the true value, expressed as $RE = \frac{\bar{\text{Δ}a}}{a}$.

Percentage Error

The relative error expressed as a percentage, calculated as \frac{\text{Δ}a}{a} \times 100\text{%}.

Propagation of Error (Exponents)

For a quantity $Y = \frac{A^x B^y}{C^z}$, the relative error is $\frac{\text{Δ}y}{y} = x\frac{\text{Δ}A}{A} + y\frac{\text{Δ}B}{B} + z\frac{\text{Δ}C}{C}$.

Least Count (LC)

The smallest value measurable by an instrument, which is considered as its absolute error.

Positive Zero Error

Occurs in Vernier Callipers when the zero of the vernier scale lies to the right of the main scale when jaws are in contact.

Negative Zero Error

Occurs in Vernier Callipers when the zero of the vernier scale lies to the left of the main scale when jaws are in contact.

Pitch

In a Screw Gauge, the distance travelled by the screw divided by the number of revolutions.