Physics Formulas MCAT (crazy style) (guaranteed A+)

Given: Initial velocity $v_0$ , final velocity $v_f$ , and time $t$ . Find: Kinematic average displacement $\Delta x$ .

$$\Delta x = \frac{v_0 + v_f}{2}t$$

Given: Change in velocity $\Delta v$ and time $t$ . Find: Acceleration $a$ .

$$a = \frac{\Delta v}{t}$$

Given: Mass $m$ and acceleration due to gravity $g$ . Find: Weight $W$ .

$$W = mg$$

Given: Masses of multiple objects $m_1, m_2, \dots$ and their positions $x_1, x_2, \dots$ . Find: Center of mass $x_{cm}$ .

$$x_{cm} = \frac{m_1x_1 + m_2x_2 + \dots}{m_1 + m_2 + \dots}$$

Given: Coefficient of kinetic friction $\mu_k$ and normal force $F_N$ . Find: Kinetic friction force $f_k$ .

$$f_k = \mu_k F_N$$

Given: Force $F$ , lever arm distance $r$ , and angle $\theta$ . Find: Torque $\tau$ .

$$\tau = rF\sin(\theta)$$

Given: Output force $F_{out}$ and input force $F_{in}$ . Find: Mechanical advantage $MA$ .

$$MA = \frac{F_{out}}{F_{in}}$$

Given: Initial kinetic and potential energy $KE_i, PE_i$ . Find: Final kinetic and potential energy $KE_f, PE_f$ in a closed system.

$$KE_i + PE_i = KE_f + PE_f$$

Given: Kinetic energy $KE$ and potential energy $PE$ . Find: Total mechanical energy $E$ .

$$E = KE + PE$$

Given: Change in total mechanical energy $\Delta E$ . Find: Work done by non-conservative forces $W_{nc}$ .

$$W_{nc} = \Delta E$$

Given: Force $F_1$ applied to an area $A_1$ in a confined fluid. Find: Resulting force $F_2$ on a second area $A_2$ .

$$\frac{F_1}{A_1} = \frac{F_2}{A_2}$$

Given: Density of fluid $\rho$ , volume $V$ , and gravity $g$ . Find: Weight of the fluid $W_{fluid}$ .

$$W_{fluid} = \rho V g$$

Given: Force $F$ applied perpendicular to a surface area $A$ . Find: Pressure $P$ .

$$P = \frac{F}{A}$$

Given: Original length $L$ , coefficient of linear expansion $\alpha$ , and change in temperature $\Delta T$ . Find: Change in length $\Delta L$ .

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

Given: Original volume $V$ , coefficient of volumetric expansion $\beta$ , and change in temperature $\Delta T$ . Find: Change in volume $\Delta V$ .

$$\Delta V = \beta V \Delta T$$

Given: Constant pressure $P$ and change in volume $\Delta V$ . Find: Work done by the gas $W$ .

$$W = P \Delta V$$

Given: Reversible heat transfer $Q$ at a constant temperature $T$ . Find: Change in entropy $\Delta S$ .

$$\Delta S = \frac{Q}{T}$$

Given: Amount of charge $\Delta q$ passing through a point over time $\Delta t$ . Find: Current $I$ .

$$I = \frac{\Delta q}{\Delta t}$$

Given: Voltage drops across individual components $V_1, V_2, \dots$ in a series circuit. Find: Total voltage $V_s$ .

$$V_s = V_1 + V_2 + \dots$$

Given: Voltage across one branch $V_1$ in a parallel circuit. Find: Total voltage $V_p$ .

$$V_p = V_1 = V_2 = \dots$$

Given: Capacitances $C_1, C_2, \dots$ connected in series. Find: Equivalent capacitance $C_{eq}$ .

$$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$$

Given: Capacitances $C_1, C_2, \dots$ connected in parallel. Find: Equivalent capacitance $C_{eq}$ .

$$C_{eq} = C_1 + C_2 + \dots$$

Given: Voltage across plates $V$ and distance between them $d$ . Find: Electric field strength in a capacitor $E$ .

$$E = \frac{V}{d}$$

Given: Current $I$ in a long straight wire and distance $r$ from the wire. Find: Magnetic field $B$ .

$$B = \frac{\mu_0 I}{2\pi r}$$

Given: Current $I$ in a circular loop of radius $r$ . Find: Magnetic field at the center of the loop $B$ .

$$B = \frac{\mu_0 I}{2r}$$

Given: Charge $q$ moving with velocity $v$ at an angle $\theta$ in a magnetic field $B$ . Find: Magnetic force $F_B$ .

$$F_B = qvB\sin(\theta)$$

Given: Current $I$ , length of wire $L$ , angle $\theta$ , and magnetic field $B$ . Find: Magnetic force on the wire $F_B$ .

$$F_B = ILB\sin(\theta)$$

Given: Frequency $f$ or period $T$ . Find: Angular frequency $\omega$ .

$$\omega = 2\pi f = \frac{2\pi}{T}$$

Given: Bulk modulus of the medium $B$ and its density $\rho$ . Find: Speed of sound $v$ .

$$v = \sqrt{\frac{B}{\rho}}$$

Given: Power of the source $P$ and the area it is spread over $A$ . Find: Wave intensity $I$ .

$$I = \frac{P}{A}$$

Given: Final intensity $I_f$ and initial intensity $I_i$ . Find: Change in sound level/decibels $\Delta \beta$ .

$$\Delta \beta = 10 \log\left(\frac{I_f}{I_i}\right)$$

Given: Length of the string/pipe $L$ and harmonic number $n = 1, 2, 3, \dots$ . Find: Wavelength for string and open pipes $\lambda$ .

$$\lambda = \frac{2L}{n}$$

Given: Length of the closed pipe $L$ and odd harmonic number $n = 1, 3, 5, \dots$ . Find: Wavelength for closed pipes $\lambda$ .

$$\lambda = \frac{4L}{n}$$

Given: Wave speed $v$ , length $L$ , and harmonic number $n = 1, 2, 3, \dots$ . Find: Frequency for string and open pipes $f$ .

$$f = \frac{nv}{2L}$$

Given: Wave speed $v$ , length $L$ , and odd harmonic number $n = 1, 3, 5, \dots$ . Find: Frequency for closed pipes $f$ .

$$f = \frac{nv}{4L}$$

Given: Slit width $a$ , order of minimum $n$ , and wavelength $\lambda$ . Find: Angle to the dark fringe in single-slit diffraction $\theta$ .

$$a \sin(\theta) = n\lambda$$

Given: Distance between slits $d$ , order $n$ , and wavelength $\lambda$ . Find: Angle to the dark fringe in double-slit interference $\theta$ .

$$d \sin(\theta) = \left(n + \frac{1}{2}\right)\lambda$$

Given: Index of refraction of the first medium $n_1$ and second medium $n_2$ . Find: Critical angle for total internal reflection $\theta_c$ .

$$\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right)$$

Given: Index of refraction $n$ and radii of curvature $R_1, R_2$ . Find: Focal length using the Lensmaker's equation $f$ .

$$\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$

Given: Focal lengths of individual lenses in contact $f_1, f_2, \dots$ . Find: Equivalent focal length $f_{eq}$ .

$$\frac{1}{f_{eq}} = \frac{1}{f_1} + \frac{1}{f_2} + \dots$$

Given: Powers of individual lenses in contact $P_1, P_2, \dots$ . Find: Equivalent power $P_{eq}$ .

$$P_{eq} = P_1 + P_2 + \dots$$

Given: Magnifications of individual lenses $m_1, m_2, \dots$ . Find: Total magnification $M_{total}$ .

$$M_{total} = m_1 \times m_2 \times \dots$$

Given: Mass $m$ and the speed of light $c$ . Find: Equivalent rest energy $E$ .

$$E = mc^2$$

Given: A parent nucleus $^{A}_{Z}X$ . Find: The products of beta-positive (positron) decay.

$$^{A}_{Z}X \rightarrow ^{A}_{Z-1}Y + e^+ + \nu_e$$

Given: An excited parent nucleus $^{A}_{Z}X^*$ . Find: The products of gamma decay.

$$^{A}_{Z}X^* \rightarrow ^{A}_{Z}X + \gamma$$

Given: A parent nucleus $^{A}_{Z}X$ absorbing an inner-shell electron $e^-$ . Find: The products of electron capture.

$$^{A}_{Z}X + e^- \rightarrow ^{A}_{Z-1}Y + \nu_e$$

Given: Decay constant $\lambda$ and number of undecayed nuclei $N$ . Find: The rate of nuclear decay $\frac{\Delta N}{\Delta t}$ .

$$\frac{\Delta N}{\Delta t} = -\lambda N$$