← Formulas
These formulas may have slightly different notation but consistent with what
I usually write.
Constants and Math formulas
\[ g=9.80\,\mbox{m/s}^2 \qquad G=6.673\times 10^{-11}\,\mbox{N}\cdot\mbox{m}^2/\mbox{kg}^2 \]
\[ ax^2+bx+c=0 \qquad x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \]
Kinematics
\begin{align} & v_x = v_{x0} + a_x \,t \\[1ex]
& x=x_0+v_{x0}\,t +\tfrac12\,a_x\,t^2 \\[1ex]
& v_x^2 = v_{x0}^2 + 2a_x\cdot(x-x_0) \\[1ex]
& \bar{v}_x = \left(\frac{v_x+v_{x0}}{2}\right)
\end{align}
Special case projectile motion:
\[
R = \frac{v_0^2\,\sin(2\theta)}{g}\qquad
T = \frac{2v_{y0}}{g} \qquad
H = \frac{v_{y0}^2}{2g}
\]
Forces
\[ (\Sigma F)_x = ma_x \]
Special formulas:
\begin{align}
& W = mg\qquad\mbox{(weight)} \\[2ex]
& F_k = \mu_k N\qquad\mbox{(kinetic friction)} \\[2ex]
& F_s \le \mu_s N\qquad\mbox{(static friction)} \\[2ex]
& F_e = -kx \qquad\mbox{($e$ for elastic, Hooke's law)} \\[2ex]
& F_g= \frac{G\,Mm}{d^2} = mg \qquad\mbox{(gravitational force, weight, def of $g$)}\\[2ex]
& a_c = \frac{v^2}{r}\qquad\mbox{(centripetal [component of] acceleration)} \\[2ex]
& (\Sigma F)_c = ma_c=\frac{mv^2}{r}\qquad\mbox{(centripetal [component of net] force)}
\end{align}
Work
\[ \mbox{Work}=Fd\cos(\theta)= \tfrac12 mv_f^2 - \tfrac12 mv_i^2 \]
\[ \mbox{Work}_{\mbox{nc}} = \Delta\,\mbox{KE} + \Delta\,\mbox{PE} \qquad\mbox{(nc=non-conservative)} \]
\[ \bar{P} = \frac{\Delta E}{\Delta t} = \frac{\mbox{Work}}{\mbox{time}}
=\frac{\mbox{Energy transformed}}{\mbox{time}}\qquad\mbox{(average power)} \]
Some types of energy:
\begin{align}
& \mbox{KE} = \tfrac12 \,mv^2 \qquad \mbox{(translational kinetic energy)}\\[2ex]
& \mbox{PE}_g = mgh \qquad \mbox{(gravitational potential energy)}\\[2ex]
& \mbox{PE}_s = \tfrac12 \,kx^2 \qquad \mbox{(elastic potential energy, spring)}\\[2ex]
\end{align}
Momentum
\begin{align}
&\vec{p} = m\vec{v}\qquad\mbox{(momentum)}\\[2ex]
&\vec{J} = (\Sigma\vec{F})(\Delta t) = \vec{p}_f - \vec{p}_i = \Delta\vec{p}=m\Delta\vec{v}
\qquad\mbox{(impulse)}\\[2ex]
&\left(v_A - v_B\right)= -\left(v_A' - v'_B\right)\qquad\mbox{(elastic collision in 1-D)}\\[2ex]
&\mbox{If $v_B=0$ then}\quad v_A'=\frac{m_A-m_B}{m_A+m_B}\cdot v_A
\qquad v_B'=\frac{2m_A}{m_A+m_B}\cdot v_A
\qquad\mbox{(inelastic collision in 1-D)}
\end{align}
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jones.3 (R Jones)
Last Modified 23:07:11 28-Feb-2022