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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Icon for the Creative Commons Attribution 4.0 International License

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

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