PHYS 201 Equation Sheets

Exam #1 Equation Sheet: Vectors and 1D Motion

$C^2 = \sqrt{A^2 + B^2}$

$\sigma = \sqrt{ \frac{1}{N-1} \sum^N_{i=1}(x_i - \overline{x})^2}$

$\delta \overline{x} = \frac{\sigma}{\sqrt{N}}$

$t' = \left| \frac{A-B}{\sqrt{\delta A^2 + \delta B^2}} \right|$

$\Delta x = x_f - x_i$

$v_{av} = \frac{\Delta x}{\Delta t}$

$v = \frac{dx}{dt}$

$a_{av} = \frac{\Delta v}{\Delta t}$

$a = \frac{dv}{dt} = \frac{d^2 x}{dt^2}$

$v_{xf} = v_{xi} + a_x t$

$v_{xf}^2 = v_{xi}^2 + 2 a_x \Delta x$

$\Delta x = v_{xi} t + \frac{1}{2} a_x t^2$

Exam #2 Equation Sheet: Projectile Motion and Forces

$v_{yf} = v_{yi} + a_y t$

$v_{yf}^2 = v_{yi}^2 + 2 a_y \Delta y$

$\Delta y = v_{yi} t + \frac{1}{2} a_y t^2$

$g = -9.81 \, {\rm{m}/\rm{s}}^2$

$F = ma$

$F_g = mg$

$F_{\rm{A\,on\,B}} = F_{\rm{B\,on\,A}}$

$F_K = \mu_K F_N$

$F_S = \mu_S F_N$

$F_D = \frac{1}{2}\, C \,A \,\rho v^2$

$v_T = \sqrt{\frac{2\, m \,g}{\rho\, A\, C}}$

Exam #3 Equation Sheet: Energy, Momentum, and Rotational Motion

$W = \vec{F} \bullet \vec{r}$

$W = F \,r \,cos \theta$

$W = F_x r_x + F_y r_y + F_z r_z$

$W = KE_f - KE_i$

$KE = \frac{1}{2} m v^2$

$PE_g = mgy$

$PE_S = \frac{1}{2} k \Delta x^2$

$F_{spring} = - k \Delta x$

$mgy_i + \frac{1}{2} m v_i^2 + \frac{1}{2} k \Delta x_i^2 + \frac{1}{2} I \omega_i^2 - F_f d = mgy_f + \frac{1}{2} m v_f^2 + \frac{1}{2} k \Delta x_f^2 + \frac{1}{2} I \omega_f^2$

$p = mv$

$m_A v_{A,i} + m_B v_{B,i} = m_A v_{A,f} + m_B v_{B,f}$

$F = \frac{dp}{dt}$

$\frac{1}{2}m_A v_{A,i}^2 + \frac{1}{2}m_B v_{B,i}^2 = \frac{1}{2}m_A v_{A,f}^2 +\frac{1}{2}m_B v_{B,f}^2$

$J = p_f - p_i$

$J = F \Delta t$

$m_A v_{A,xi} + m_B v_{B,xi} = m_A v_{A,xf} + m_B v_{B,xf}$

$m_A v_{A,yi} + m_B v_{B,yi} = m_A v_{A,yf} + m_B v_{B,yf}$

$v_{Af} = \frac{2 m_B v_{B,i} + (m_A - m_B) v_{A,i}}{m_A + m_B}$

$v_{Bf} = \frac{2 m_A v_{A,i} + (m_B - m_A) v_{B,i}}{m_A + m_B}$

$\omega_f = \omega_i + \alpha t$

$\omega_f^2 = \omega_i^2 + 2 \alpha \Delta \theta$

$\Delta \theta = \omega_i t + \frac{1}{2} \alpha t^2$

$s = \Delta \theta r$

$v = \omega r$

$a = \alpha r$

$F_c = \frac{m v^2}{r}$

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

$\vec{\tau} = \vec{r} \times \vec{F}$

$\tau = r F sin(\theta)$

$\tau = I \alpha$

$\vec{\tau} = (r_y F_z - r_z F_y) \hat{i} + (r_z F_x - r_x F_z ) \hat{j} + (r_x F_y - r_y F_x) \hat{k}$

$x_{cm} = \frac{\sum\limits_{i=1}^N m_i \, x_i}{\sum\limits_{i=1}^N m_i}$

$y_{cm} = \frac{\sum\limits_{i=1}^N m_i \, y_i}{\sum\limits_{i=1}^N m_i}$

$I_{\rm point\, particle} = m r^2$

$I_{total} = \sum I_i$

$L = m\, v\, r\, sin \theta$

$L = I\, \omega$

$L_i = L_f$

$m\, v_i\, r_i\, sin\theta + I_i \,\omega_i = m\, v_f\, r_f\, sin\theta + I_f \,\omega_$

$KE_{rot} = \frac{1}{2} I \omega^2$

Final Exam Equation Sheet: Fluid Mechanics and Thermodynamics

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

$p = p_0 + \rho \, g \, \Delta y$

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

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

$F_B = m_{fluid} \,g$

$A_1 v_1 = A_2 v_2$

$p_1 + \rho g h_1 + \frac{1}{2} \rho v_1^2 = p_2 + \rho g h_2 + \frac{1}{2} \rho v_2^2$

$T_F = \frac{9}{5} T_C + 32$

$T_C = \frac{5}{9} (T_F - 32)$

$T_K = T_C + 273$

$\Delta L = L_0 \,\alpha \,\Delta T$

$Q = m \, c \, \Delta T$

$Q = m L_F$

$Q = m L_V$

$\sum Q = 0$

$P = \frac{E}{t}$

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Introductory Physics Resources Copyright © by Adria C Updike is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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