IMG_7886.HEIC

# Physics ## Kinematics ### Useful Quantities * **Displacement** $\Delta x = x_{f} - x_{i}$ * **Average velocity** $v_{avg} = \frac{\Delta x}{\Delta t}$ * **Average acceleration** $a_{avg} = \frac{\Delta v}{\Delta t}$ ### Constant Acceleration * $v = v_{0} + at$ * $x =...

# Physics ## Kinematics ### Useful Quantities * **Displacement** $\Delta x = x_{f} - x_{i}$ * **Average velocity** $v_{avg} = \frac{\Delta x}{\Delta t}$ * **Average acceleration** $a_{avg} = \frac{\Delta v}{\Delta t}$ ### Constant Acceleration * $v = v_{0} + at$ * $x = x_{0} + v_{0}t + \frac{1}{2}at^{2}$ * $v^{2} = v_{0}^{2} + 2a(x - x_{0})$ * $x - x_{0} = \frac{1}{2}(v + v_{0})t$ * $x - x_{0} = vt - \frac{1}{2}at^{2}$ ### Projectile Motion * $v_{0x} = v_{0}cos\theta$ * $v_{0y} = v_{0}sin\theta$ * $v_{x} = v_{0}cos\theta$ * $v_{y} = v_{0}sin\theta - gt$ * $x = v_{0}cos\theta t$ * $y = v_{0}sin\theta t - \frac{1}{2}gt^{2}$ ## Dynamics ### Useful Quantities * **Force** $\overrightarrow{F}$ is a push or pull on an object * **Mass** m is the measure of an object's resistance to acceleration * **Weight** $F_{g} = mg$ * **Newton's Second Law** $\overrightarrow{F}_{net} = m\overrightarrow{a}$ * **Friction** * Static: $f_{s} \leq \mu_{s}F_{N}$ * Kinetic: $f_{k} = \mu_{k}F_{N}$ ### Uniform Circular Motion * $a_{c} = \frac{v^{2}}{r}$ * $v = \frac{2\pi r}{T}$ ## Energy ### Useful Quantities * **Work** $W = \overrightarrow{F} \cdot \overrightarrow{\Delta x} = F\Delta xcos\theta$ * **Kinetic Energy** $K = \frac{1}{2}mv^{2}$ * **Potential Energy** * Gravitational: $U_{g} = mgy$ * Spring: $U_{s} = \frac{1}{2}kx^{2}$ * **Work-Energy Theorem** $W_{net} = \Delta K$ * **Power** $P = \frac{W}{\Delta t} = \overrightarrow{F} \cdot \overrightarrow{v}$ ### Conservation of Energy * $E = K + U$ * $\Delta E = 0$ * $W_{nc} = \Delta E$ ## Momentum ### Useful Quantities * **Momentum** $\overrightarrow{p} = m\overrightarrow{v}$ * **Impulse** $\overrightarrow{I} = \overrightarrow{F}\Delta t = \Delta\overrightarrow{p}$ * **Conservation of Momentum** $\Delta \overrightarrow{p} = 0$ ### Collisions * **Elastic** * Momentum is conserved * Kinetic energy is conserved * **Inelastic** * Momentum is conserved * Kinetic energy is NOT conserved ## Rotation ### Useful Quantities * **Angular displacement** $\Delta \theta = \theta_{f} - \theta_{i}$ * **Angular velocity** $\omega = \frac{\Delta \theta}{\Delta t}$ * **Angular acceleration** $\alpha = \frac{\Delta \omega}{\Delta t}$ * **Torque** $\tau = rFsin\theta$ * **Moment of inertia** $I = \sum mr^{2}$ * **Angular momentum** $L = I\omega$ * **Rotational Kinetic Energy** $K = \frac{1}{2}I\omega^{2}$ ### Relations * $s = r\theta$ * $v = r\omega$ * $a = r\alpha$ ### Constant Angular Acceleration * $\omega = \omega_{0} + \alpha t$ * $\theta = \theta_{0} + \omega_{0}t + \frac{1}{2}\alpha t^{2}$ * $\omega^{2} = \omega_{0}^{2} + 2\alpha(\theta - \theta_{0})$ * $\theta - \theta_{0} = \frac{1}{2}(\omega + \omega_{0})t$ * $\theta - \theta_{0} = \omega t - \frac{1}{2}\alpha t^{2}$ ### Conservation of Angular Momentum * $\Delta L = 0$ ## Oscillations ### Useful Quantities * **Period** T is the time for one oscillation * **Frequency** $f = \frac{1}{T}$ * **Angular Frequency** $\omega = 2\pi f$ ### Simple Harmonic Motion * $x = Acos(\omega t + \phi)$ * $v = -A\omega sin(\omega t + \phi)$ * $a = -A\omega^{2} cos(\omega t + \phi)$ * $\omega = \sqrt{\frac{k}{m}}$ * $T = 2\pi \sqrt{\frac{m}{k}}$ ### Pendulums * Simple: $T = 2\pi \sqrt{\frac{L}{g}}$ * Physical: $T = 2\pi \sqrt{\frac{I}{mgd}}$ ## Waves ### Useful Quantities * $v = f\lambda$ ### Superposition * $y = y_{1} + y_{2}$ ### Standing Waves * $f_{n} = n\frac{v}{2L}$ * $f_{n} = n\frac{v}{4L}$ ## Thermodynamics ### Useful Quantities * **Temperature** * $T_{C} = T - 273.15$ * $T_{F} = \frac{9}{5}T_{C} + 32$ * **Thermal Expansion** * Linear: $\Delta L = \alpha L_{0} \Delta T$ * Volume: $\Delta V = \beta V_{0} \Delta T$ * **Heat** $Q = mc\Delta T$ $Q = mL$ ### Ideal Gas Law * $PV = nRT$ * $R = 8.314 \frac{J}{mol \cdot K}$ * $K_{avg} = \frac{3}{2}k_{B}T$ * $v_{rms} = \sqrt{\frac{3RT}{M}}$ ### Laws of Thermodynamics * $Q = \Delta U + W$ * $e = \frac{W}{Q_{H}}$ * $e_{c} = 1 - \frac{T_{C}}{T_{H}}$