Engineering Component Mathematics and Logarithms

This set of flashcards covers engineering mathematics including circular arc calculations, degree-to-radian conversions, and the application of logarithm laws.

Degree to Radians Conversion Formula

The process of converting degrees to radians by multiplying the value in degrees by $\frac{\pi}{180}$.

Radian value of $110^{\circ}$

Approximately $1.92\,\text{rads}$, calculated from $\frac{110 \times \pi}{180}$.

Arc Length Formula

$s = r\theta$, where $s$ is the arc length, $r$ is the radius, and $\theta$ is the angle measured in radians.

Arc length for point A to B

$153.59\,\text{mm}$, calculated using a radius of $80\,\text{mm}$ and an angle of $1.92\,\text{rads}$ ($80 \times 1.92$).

Total Noise Formula ($N$)

$N = \log(7) + 2\log(3)$, which represents the total noise produced by two compressors.

Logarithm Power Law

A law of logarithms where $n\log(x) = \log(x^n)$, used to simplify $2\log(3)$ into $\log(3^2)$ or $\log(9)$.

Logarithm Product Law

A law of logarithms where $\log(x) + \log(y) = \log(x \times y)$, used to combine $\log(7) + \log(9)$ into a single logarithm.

Simplified Noise Equation ($N$)

The single logarithm expression $N = \log(63)$, derived from simplifying $\log(7) + \log(9)$.