Formula | Note |
---|---|

$$v = \frac{d}{\Delta t}$$ | Calculate constant velocity. |

$$v_f = v_i +at$$ | Change in velocity is equal to acceleration x time. |

$$\Delta d = v_it + \frac{1}{2}at^2$$ | Quadratic equation for object undergoing acceleration. |

$$t=\frac{-V_i \pm \sqrt{V_i^2+2a \Delta d}}{a}$$ | Quadratic formula, time when projectile hits the ground. |

$$\Delta d = \frac{v_i+v_f}{2}$$ | Find distance travelled based on acerage velocity. |

$$t=\sqrt{\frac{2 \Delta d}{a}}$$ | If initial velocity is zero, easy way to solve for time. |

$$v_f^2 = v_i^2+2a \Delta d$$ | Square proportionality between both velocities, acceleration and distance travelled. |

Formula | Note |
---|---|

$$a = \frac{F_{net}}{m}$$ | Newton's second law. |

$$F_g = mg$$ | This is weight. 'g' is the gravitational constant, which is why you weigh differently on the moon! |

$$F_N = -mg$$ | Normal force, acts perpendicular to weight. Example, exerted by table on book to keep it on the table. |

$$F_f = \mu F_N$$ | Friction force, acts opposite to motion of an object. |

$$F_s = -k \Delta x$$ | Spring force which is proportional to negative displacement of an object since it tries to reach equilibrium. |

$$\mu_s = \tan \theta$$ | Find static coefficient of friction of an object on an inclined plane, theta being the angle when the object begins to slide. |

$$F_x = mg \sin \theta$$ | Force parralel to incline plane, moving the object. |

$$F_y = mg \cos \theta$$ | Force perpendicular to incline plane. |

$$F_{on1by2} = -F_{on2by1}$$ | Newton's third law of motion. |

$$W = F \Delta d$$ | Work done by an object. |

$$W = F \Delta d \cos \theta$$ | Work done by an object force is acting at an angle. |

$$F_T = ma = Ma$$ | Frictionless pulley with two objects attached on a string. |

$$a = \frac{M_g - m_g}{m+M}$$ | Find acceleration of objects on a pulley. |

$$PE_g = mgh$$ | Potential gravitational energy. |

$$KE = \frac{1}{2}mv^2$$ | Kinetic energy. |

$$PE_{el} = \frac{1}{2}k \Delta x^2$$ | Potential elastic energy. |

$$W = \Delta KE + \Delta PE_g + \Delta PE_e$$ | Change in mechanical energy is work. |

$$h = L(1-\cos \theta)$$ | Vertical height of pendulum string. |

$$P = \frac{W}{t} = Fv$$ | Power of an object. |

$$e = \frac{P_{out}}{P_{in}}$$ | Efficiency of a mechanical system. |

$$p = mv$$ | Momentum of an object. |

$$F = \frac{\Delta p}{\Delta t} = m(\frac{v_f-v_i}{t})$$ | Newton's second law. |

$$\Delta p = F \Delta t$$ | Impulse-momentum formula. |

$$m_1v_{i1} + m_2v_{i2} = m_1v_{f1} + m_2v_{f2}$$ | Perfectly elastic collisions. |

$$m_1v_1 + m_2v_2 = v_f(m_1+m_2)$$ | Perfectly inelastic collisions. Objects move at same speed before or after collision. |

Formula | Note |
---|---|

$$Q = mc \Delta T$$ | Energy, or heat, in a medium of set mass. |

$$Q_{latent} = mL$$ | Latent heat of an object as it goes through phase changes. |

$$Q_1 = -Q_2$$ | Heat gained by one object is lost by the other object. |

$$PV=nRT$$ | Relationship between pressure, volume, and temperature in an ideal gas. |

$$PV = NK_BT$$ | Same as previous formula but using Boltzman's constant. |

$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$ | Derivation of what happens to a a set object when it changes pressure, temperature, or volume. |

$$P=\frac{F}{A}$$ | Formula for pressure acting on a given surface. |

$$PV = \frac{N}{3}mv^2$$ | Theoretical equation of an ideal gas. |

$$KE = \frac{3}{2}K_BT$$ | Average kinetic energy of molecules in an ideal gas. |

$$v = \sqrt{\frac{3K_BT}{m}}$$ | Mean value of speed of molecules in an ideal gas. |

Formula | Note |
---|---|

$$\Delta x = x_0 \cos (\omega t)$$ | Displacement of an oscillating object. |

$$\omega = 2 \pi f$$ | Speed of wave. |

$$\omega^2 = \frac{k}{m}$$ | Speed of wave in an elastic string. |

$$T = \frac{1}{f} \rightarrow f = \frac{1}{T}$$ | Relationship between frequency and time. |

$$a = -{\omega}^2x$$ | Current acceleration. |

$$a_{max} = -{\omega}x_0$$ | Maximum acceleration. |

$$v_{max} = \omega x_0$$ | Maximum velocity. |

$$v(t) = -x_0 \omega \sin (\omega t)$$ | Velocity as a function of time. |

$$a(t) = x_0 \cos (\omega t)$$ | Acceleration as a function of time. |

$$KE(t) = \frac{1}{2}mx_0^2 {\omega}^2 \sin (\omega t)$$ | Kinetic energy as a function of time. |

$$PE_{elastic}(t) = \frac{1}{2}kx_0^2 {\cos}^2 (\omega t)$$ | Potential elastic energy as a function of time. |

$$\lvert \Delta d \rvert = n \lambda$$ | Path difference for constructive interference of double slit. |

$$\lvert \Delta d \rvert = (n+\frac{1}{2}) \lambda$$ | Path difference for destructive interference of double slit. |

$$d \sin \theta = n \lambda$$ | Local maximum of intensity acting on a wall after a double slit. |

$$\frac{S}{D} = \frac{n \lambda}{d}$$ | Small angle approximation derived from previous formula. |

$$\theta_i = \theta_r$$ | Angle of incident is equal to angle of reflection. |

$$n_1 \sin \theta_i = n_2 \sin \theta_r$$ | Snell's law for angle of refraction. |

$$\sin \theta_c = \frac{n_2}{n_1}$$ | Snell's law when $\theta_r = 90°$ for critical angle of refraction. |

$$n = \frac{c}{v}$$ | Refractive index of a wave. Higher index means wave travels slower in a given medium. |

$$b \sin \theta = \frac{n \lambda}{b}$$ | Destructive interference in a single slit. |

$$I \propto A^2$$ | Intensity is related to the square of the amplitude of the wave. |

$$I \propto x^{-2}$$ | If distance from source increases, intensity decreases by the square of that. |

$$I = I_0 \cos^2 \theta$$ | Intensity of a polarized light source, maximum at $n\pi, n \in \mathbb{N}$. |

Formula | Note |
---|---|

$$F = k \frac{q_1q_2}{r^2}$$ | Coulomb's Law. The electric force between two charges, seperated by distance r. What's $k$, you may ask? |

$$k = \frac{1}{4\pi\varepsilon_0} \approx 8.99 Nm^2C^{-2}$$ | Coulomb constant, defined in terms of the permittivity of free space. |

$$W=Vq$$ | Work done (energy) by a particle is equal to the voltage times the charge. |

$$E = \frac{F}{q_2} = \frac{q_1}{r^2}$$ | Electric field strength acting on a charge. Divide by the charge of which you are finding the field strength. |

$$I = nAvq \rightarrow v = \frac{I}{nAq}$$ | More details on current in terms of the velocity of the electrons, the right formula will come in handy to calculate their speed! |

$$I = \frac{\Delta q}{\Delta t}$$ | Current is the rate of change of charge (how fast/many electrons are flowing). |

$$V = IR$$ | Ohm's Law. Beautiful. In an ohmic system, voltage is the product of current times resistance. |

$$\Sigma V = 0$$ | Kirchhoff's voltage law, sum of all voltages across any loop in a circuit will be 0. |

$$\Sigma I = 0$$ | Kirchhoff's current law, sum of all current intering a node equals the sum of all current leaving the node. |

$$P = VI = I^2R = \frac{V^2}{R}$$ | Power dissipated in a source of resistance (joule heating) |

$$R_{total} = \Sigma R = R_1 + R_2 + ...$$ | Sum resistance when resistors are IN SERIES (same wire). |

$$R_{total} = \frac{1}{\Sigma \frac{1}{R}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + ...}$$ | Sum reciprocal resistance when resistors are IN PARALLEL (seperated by node). |

$$\delta = \frac{RA}{L} = \frac{R\pi r^2}{L}$$ | Resistivity equals resistance times cross sectional area of wire divided by length of wire. |

$$\varepsilon = I(R + r) \rightarrow V = \varepsilon - Ir$$ | Internal resistance of a battery cell, notably the output voltage DECREASES when current INCREASES. |

$$F = qvB \sin \theta$$ | Lorentz force for a particle in a magnetic field of charge $q$ and velocity $v$, where $\theta$ is the angle to the normal (they will try and trick you with this, force is highest when at a right angle!) |

$$F = BIL \sin \theta$$ | Lorentz force for wire of length $L$ and current $I$, where $\theta$ is the angle to the normal (they will try and trick you with this, force is highest when at a right angle!) |