Physics and Engineering Fundamentals Flashcards

Comprehensive vocabulary flashcards covering constants, mechanics, thermodynamics, and electromagnetism based on the provided lecture notes.

$c$ (Speed of light)

$$3.0 \times 10^8\,m/s$$

$R$ (Gas constant)

$$8.314\,J/(mol\,K)$$

$k_B$ (Boltzmann constant)

$$1.38 \times 10^{-23}\,J/K$$

$N_A$ (Avogadro's number)

$$6.023 \times 10^{23}\,molecules/mole$$

$m_p$ (Mass of a proton)

$$1.67 \times 10^{-27}\,kg$$

$m_e$ (Mass of an electron)

$$9.11 \times 10^{-31}\,kg$$

Speed of sound in air

$$343\,m/s$$

Density of water

$$1.00 \times 10^3\,kg/m^3$$

Specific heat of water

$$4.2 \times 10^3\,J/(kg\,K)$$

Specific heat of ice

$$2.1 \times 10^3\,J/(kg\,K)$$

Latent heat of fusion of water

$$330 \times 10^3\,J/kg$$

Latent heat of vaporisation of water

$$2260 \times 10^3\,J/kg$$

Atmospheric pressure

$$1.013 \times 10^5\,Pa$$

Atmospheric density

1.21 kg/m3

$g$ (Acceleration due to gravity)

$$9.80\,m/s^2$$

$G$ (Gravitational constant)

$$6.67 \times 10^{-11}\,N\,m^2/kg^2$$

$\sigma$ (Stefan Boltzmann constant)

$$5.67 \times 10^{-8}\,W/(m^2\,K^4)$$

$e$ (Elementary charge)

$$1.60 \times 10^{-19}\,C$$

$k_e$ (Couloumb constant)

$$8.99 \times 10^9\,Nm^2/C^2$$

$\varepsilon_o$ (Permittivity constant)

$$8.85 \times 10^{-12}\,F/m$$

$\mu_o$ (Permeability constant)

$$1.26 \times 10^{-6}\,H/m$$

Newton's Second Law

$$\vec{F} = m\vec{a} = \frac{d\vec{p}}{dt}$$

Linear momentum ($\vec{p}$)

$$\vec{p} = m\vec{v}$$

Hooke's Law (Spring Force)

$$F_{spring} = -kx$$

Impulse

$$\Delta p$$

Kinetic Friction

$$F_{kinetic} = \mu_k N$$

Kinematic equation for velocity (constant acceleration)

$$v = v_0 + at$$

Kinematic equation for displacement (constant acceleration)

$$\Delta x = v_0t + \frac{1}{2}at^2$$

Work ($W$)

$$W = \int \vec{F} \cdot d\vec{s}$$

Spring Potential Energy ($U_{spring}$)

$$\frac{1}{2}kx^2$$

Kinetic Energy ($KE$)

$$\frac{1}{2}mv^2$$

Centripetal acceleration ($a_{cent}$)

$$\frac{v^2}{r} = \omega^2 r$$

Torque ($\vec{\tau}$)

$\vec{\tau} = \vec{r} \times \vec{F}$ or $\tau = rF \sin(\theta)$ or $\tau = I\alpha$

Angular Momentum ($\vec{L}$)

$\vec{L} = \vec{r} \times \vec{p}$ or $L = I\omega$

Rotational Kinetic Energy

$$\frac{1}{2}I\omega^2$$

Parallel Axis Theorem

$$I_D = I_{CM} + MD^2$$

Moment of inertia (Hoop)

$$I_{hoop} = MR^2$$

Moment of inertia (Disc)

$$I_{disc} = \frac{1}{2}MR^2$$

Moment of inertia (Rod)

$$I_{rod} = \frac{1}{12}MR^2$$

Density (Mechanics definition)

$$\rho = \frac{m}{V}$$

Heat ($Q$)

$Q = mC\Delta T$ or $Q = mL$

Linear expansion ($\Delta L$)

$$\Delta L = \alpha L\Delta T$$

Thermal conductivity (Power transfer)

$$P = kA\frac{dT}{dx}$$

Radiation (Stefan-Boltzmann Law)

$$P = \varepsilon \sigma AT^4$$

Ideal gas law

$$PV = nRT = N k_B T = \frac{1}{3} Nmv_{rms}^2$$

Molar specific heats (Monatomic gas)

$C_V = \frac{3}{2}R$, $C_P = \frac{5}{2}R$

Molar specific heats (Diatomic gas)

$C_V = \frac{5}{2}R$, $C_P = \frac{7}{2}R$

First law of thermodynamics

$$\Delta E_{int} = Q + W$$

Adiabatic relations

$PV^{\gamma} = \text{constant}$, $TV^{\gamma-1} = \text{constant}$, where $\gamma = \frac{C_p}{C_V}$

Root mean square gas velocity ($v_{rms}$)

$$\sqrt{\frac{3RT}{M}}$$

Thermodynamic Work ($dW$)

$$dW = -P dV$$

Engine Efficiency (General)

$$\varepsilon = \frac{|W|}{Q_H} = 1 - \frac{|Q_C|}{|Q_H|}$$

Entropy (Change)

$$\Delta S = \int \frac{dQ_{rev}}{T}$$

Carnot Efficiency ($\varepsilon_C$)

$$\varepsilon_C = 1 - \frac{T_C}{T_H}$$

Ohm's Law (Resistance)

$$R = \frac{\Delta V}{I}$$

Resistivity definition ($R$ to $\rho$)

$$R = \frac{\rho L}{A}$$

Capacitance ($C$)

$$C = \frac{Q}{\Delta V}$$

Parallel plate capacitance

$$C = \frac{\kappa \varepsilon_o A}{d}$$

Energy stored in Capacitor ($U$)

$$U = \frac{1}{2}Q\Delta V = \frac{1}{2}C(\Delta V)^2 = \frac{1}{2}\frac{Q^2}{C}$$

Coulumb's Law (Electric Force)

$$F_e = k_e \frac{q_1q_2}{r^2} = \frac{q_1q_2}{4\pi\varepsilon_or^2}$$

Electric Field ($E$)

$$E = k_e \frac{q}{r^2} = \frac{q}{4\pi\varepsilon_or^2}$$

Electrical Power ($P$)

$$P = I\Delta V = I^2R = \frac{\Delta V^2}{R}$$

Potential difference ($\Delta V$)

$$\Delta V = V_b - V_a = - \int_a^b \vec{E} \cdot \vec{ds}$$

Biot-Savart Law (differential magnetic field)

$$d\vec{B} = \frac{\mu_o}{4\pi} \frac{Id\vec{s} \times \vec{r}}{r^2}$$

Magnetic Force (Lorenz force)

$$\vec{F}_B = q\vec{v} \times \vec{B}$$

Radius of orbit in magnetic field

$$r = \frac{mv}{qB}$$

Magnetic Flux ($\Phi_B$)

$$\Phi_B = \int \vec{B} \cdot d\vec{A}$$

Faraday's Law of Induction

$$\varepsilon = -\frac{d\Phi_B}{dt}$$