Comprehensive Engineering and Science Review

Flashcards covering key mathematical formulas, scientific principles, material properties, and electrical concepts from the engineering lecture notes.

Volume of a cylinder

$$V = \pi r^2 h$$

Gradient

The slope of a line, calculated as $\frac{\text{rise}}{\text{run}}$.

y-intercept

The point where a straight line graph crosses the y-axis, represented by the variable $c$ in the equation $y = mx + c$.

Differentiation

A mathematical process used to find the rate of change or gradient.

Integration

The opposite of differentiation; its core rule is $\int x^n dx = \frac{x^{n+1}}{n+1} + C$.

Hypotenuse

The side labeled $c$ in the Pythagorean theorem $a^2 + b^2 = c^2$, representing the longest side of a right-angled triangle.

Secant ($\sec \theta$)

A reciprocal trigonometric function defined as $\frac{1}{\cos \theta}$.

Sine rule

A rule used when a triangle is not right-angled and an angle and opposite side pair are known: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$.

Cosine rule

Used to find a missing side when no right angle is present: $a^2 = b^2 + c^2 - 2bc \cos A$.

Radians

A circular measure where a full circle equals $2\pi$ radians.

Arc length ($s$)

$$s = r\theta$$

Vector

A quantity that has both magnitude and direction.

Scalar

A quantity that has magnitude only.

Standard deviation

A measure of the spread of data; population formula: $\sigma = \sqrt{\frac{\sum f(x_i - \bar{x})^2}{n}}$.

Mole (mol)

The SI unit for the amount of substance.

Acceleration

The rate of change of velocity, calculated as $a = \frac{\Delta v}{t}$ or $\frac{\text{final velocity} - \text{initial velocity}}{\text{time}}$; the SI unit is $m/s^2$.

Polar coordinates

Coordinates expressed as $(r, \theta)$, where $r$ is the distance from the origin and $\theta$ is the angle.

Hypothesis

A testable prediction used in the scientific method.

Calibration

The process of checking equipment against a known standard to improve accuracy and reduce errors.

Molecules

Two or more atoms chemically bonded together.

Electrolyte

A liquid that conducts electricity.

Anode

An electrode with a positive charge ($+$).

Alloys

A mixture of metals.

Pressure ($P$)

Force per unit area, calculated as $P = \frac{F}{A}$; measured in Pascal ($Pa$).

Moments

The turning effect of a force, calculated as $M = F \times d$ with the unit $Nm$.

Newton's First Law

If no net force acts, stationary objects stay still and moving objects continue at a constant speed.

Viscosity

The resistance of a fluid to flow.

Bernoulli's principle

As fluid speed increases, pressure decreases; as fluid speed decreases, pressure increases.

Conduction

Heat transfer by direct contact.

Isolated system

A thermodynamic system that transfers neither mass nor energy.

Sensible heat

Heat causing temperature change without phase change; formula: $Q = mc\Delta T$.

Boyle's Law

At constant temperature, pressure and volume are inversely related: $P_1V_1 = P_2V_2$.

Charles' Law

At constant pressure, temperature and volume are directly proportional: $$\frac{V_1}{T_1} = \frac{V_2}{T_2}$ houses a constant.

Specific heat capacity

Energy needed to raise $1\,kg$ of material by $1\,^{\circ}C$.

Tensile stress

A type of stress caused by pulling forces.

Ferrous metals

Metals containing iron, such as low-carbon steel or cast iron.

Sintering

A process where metal powder is heated below its melting point until particles fuse together.

Quenching

Rapid cooling of a material in oil or water to alter its crystal structure.

Stress

Force applied per unit area, calculated as $\sigma = \frac{F}{A}$.

Young's modulus ($E$)

A measure of elasticity calculated as $E = \frac{\text{stress}}{\text{strain}}$.

Newton's Third Law

For every action, there is an equal and opposite reaction.

Conservation of Momentum

Momentum cannot be created or destroyed unless an external force acts; formula: $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$.

D'Alembert's principle

An alternative form of Newton's second law: $F - ma = 0$.

Mechanical work ($W$)

Energy transferred by a force, calculated as $W = Fd$ and measured in Joules ($J$).

Biofuels

Fuel made from biomass that replaces fossil fuels to reduce carbon emissions.

Magnetic flux ($\phi$)

The total magnetic field passing through an area, measured in weber ($Wb$).

AC (Alternating Current)

Current that changes direction continuously, typically used in mains electricity.

Multimeter

A device used to measure voltage, current, and resistance.