\begin{equation} \sum \vec{ \textbf{F}} = \textbf{0} \qquad ( \textnormal{equilibrium, vector form}) \tag{6.1} \end{equation} \begin{equation} \sum F_{x} = 0 \qquad \sum F_{y} = 0 \qquad \textnormal{(equilibrium, component form)} \tag{6.2} \end{equation} \begin{equation} \sum \vec{ \textbf{F}} = m \vec{ \textbf{a}} \qquad (\textnormal{Newton's second law, vectors}) \tag{6.3} \end{equation} \begin{equation} \sum F_{x} = m a_x \qquad \sum F_{y} = m a_y \qquad \sum F_{z} = m a_z \qquad \textnormal{(Newton's second law, components)} \tag{6.4} \end{equation} \begin{equation} f = \mu_k \, n \qquad \textnormal{(Magnitude of kinetic friction)} \tag{6.5} \end{equation} \begin{equation} f_s \leq \mu_s \, n \qquad \textnormal{(Magnitude of static friction)} \tag{6.6} \end{equation} \begin{equation} a_{rad} = \frac{v^2}{R} \qquad \textnormal{(centripetal acceleration, circular motion)} \tag{6.7} \end{equation} \begin{equation} a_{rad} = \frac{4 \pi^2 R}{T^2} \qquad \textnormal{(centripetal acceleration, circular motion)} \tag{6.8} \end{equation}
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