## PHYS 191 Equations

For all assessments, I will give you the following equations.  If there is an equation you think you need but it isn’t on here, you need to memorize it.  (you should memorize Newton’s second law, the definition of average velocity and acceleration)

$F=G\frac{m_1 m_2}{r^2}$   $f_s \le \mu_s N$  $f_k = \mu_k N$

$\vec{W} = m\vec{g}$

$\Delta x = v_{ix} \Delta t +\frac{1}{2}a_x (\Delta t)^2$

$v_{fx}^2 =v_{ix}^2 + 2a_x \Delta x$

$s=r\theta$             $v=r\omega$      $a=r\alpha$

$\Delta \theta = \omega_0 \Delta t +\frac{1}{2}\alpha (\Delta t)^2$

$\omega^2 = \omega_0^2 +2\alpha \Delta \theta$

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

$W = F\Delta r \cos \theta$     $W = \Delta E$

$K = \frac{1}{2}mv^2$

$\Delta U_g = mg\Delta y$  $U_G = \frac{-Gm_1 m_2}{r}$

$F_\text{spring} = ks$  $\Delta U_\text{spring} = \frac{1}{2} ks^2$

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

$\vec{p} = m\vec{v}$  $x_{cm} = \frac{\sum_i m_i x_i}{\sum_i m_i}$

$K_\text{rot} = \frac{1}{2} I \omega^2$  $I = \sum_i m_i r_i^2$

$\tau = rF \sin \theta$   $L = I\omega$

$\tau_\text{net-o} = \frac{\Delta L}{\Delta t}$

$\vec{p}=m\vec{v}$  $x_{CM} = \frac{m_1 x_1 + m_2 x_2+...m_N x_N}{M}$

Constants

$G = 6.67 \times 10^{-11} \text{ N*m}^2\text{/kg}^2$

$\vec{g} = -9.8\hat{y} \text{ N/kg}$

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