Code: Select all
\begin{gather*}
\textbf{Impulse }I = F\Delta t = \int_{t_1}^{t_2} F dt = m\Delta v = \Delta p\\
\textbf{moment of inertia } I=\int r^2 dm = \int (x^2+y^2) dm = \sum_i {r_i}^2 m_i\\
\end{gather*}
Code: Select all
\begin{gather*}
\textbf{Impulse }I = F\Delta t = \int_{t_1}^{t_2} F dt = m\Delta v = \Delta p\\
\textbf{moment of inertia } I=\int r^2 dm = \int (x^2+y^2) dm = \sum_i {r_i}^2 m_i\\
\end{gather*}
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Code: Select all
\begin{align*}
\textbf{Impulse } I &= F\,\Delta t = \int_{t_1}^{t_2} F\,dt = m\,\Delta v = \Delta p \\
\textbf{moment of inertia } I &= \int r^2\,dm = \int (x^2+y^2)\,dm = \sum_i {r_i}^2 m_i \\
\end{align*}
Code: Select all
\documentclass[fleqn]{amsart}
\usepackage[lmargin=1cm, rmargin=1cm, tmargin=1cm, bmargin=1cm]{geometry}
\title{Equations}
\setlength{\mathindent}{0pt}
\begin{document}
\begin{align*}
v_f=v_0+at\\
\Delta x= v_0 t+\frac{1}{2}at^2\\
{v_f}^2={v_0}^2+2a\Delta x\\
x_{cm}=\frac{\sum_{i} x_i m_i}{M} = \int x dm \\
\tau = rF\sin\phi\\
\textbf{Drag} = \frac{1}{4} Av^2\\
KE=\frac{1}{2} mv^2\\
PE=mgy\\
{PE}_s = \frac{1}{2}kx^2\\
F_s=-kx\\
W=F_{||}d=Fd\cos \theta = \int F dx\\
\textbf{Impulse }I = F\Delta t = \int_{t_1}^{t_2} F dt = m\Delta v = \Delta p\\
\textbf{moment of inertia } I=\int r^2 dm = \int (x^2+y^2) dm = \sum_i {r_i}^2 m_i\\
\omega =\frac{\Delta \theta}{\Delta t}=\frac{d\theta}{dt}\\
v_t=\omega r\\
a_t=\alpha r\\
a_r=\frac{v^2}{r}\\
\mbox{Range}=\frac{{v_0}^2}{g}\sin 2\theta\\
F_G = G \frac{m_1 m_2}{r^2}\mbox{, } G=6.67\times 10^{-11} N\cdot m^2/{kg}^2
\end{align*}
\end{document}
Code: Select all
\documentclass[fleqn]{amsart}
\usepackage[lmargin=1cm, rmargin=1cm, tmargin=1cm, bmargin=1cm]{geometry}
\title{Equations}
\setlength{\mathindent}{0pt}
\begin{document}
\begin{gather*}
v_f=v_0+at\\
\Delta x= v_0 t+\frac{1}{2}at^2\\
{v_f}^2={v_0}^2+2a\Delta x\\
x_{cm}=\frac{\sum_{i} x_i m_i}{M} = \int x dm \\
\tau = rF\sin\phi\\
\text{\bfseries Drag} = \frac{1}{4} Av^2\\
KE=\frac{1}{2} mv^2\\
PE=mgy\\
{PE}_s = \frac{1}{2}kx^2\\
F_s=-kx\\
W=F_{||}d=Fd\cos \theta = \int F dx\\
\text{\bfseries Impulse }I = F\Delta t = \int_{t_1}^{t_2} F dt = m\Delta v = \Delta p\\
\text{\bfseries Moment of inertia } I=\int r^2 dm = \int (x^2+y^2) dm = \sum_i {r_i}^2
m_i\\
\omega =\frac{\Delta \theta}{\Delta t}=\frac{d\theta}{dt}\\
v_t=\omega r\\
a_t=\alpha r\\
a_r=\frac{v^2}{r}\\
\mbox{Range}=\frac{{v_0}^2}{g}\sin 2\theta\\
F_G = G \frac{m_1 m_2}{r^2}\mbox{, } G=6.67\times 10^{-11} N\cdot m^2/{kg}^2
\end{gather*}
\end{document}
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