\begin{equation} \omega = \lim_{\Delta t\to 0} \frac{\Delta \theta}{\Delta t} = \frac{d \theta}{dt} \qquad (\textnormal{Angular velocity}) \tag{10.1} \end{equation} \begin{equation} \alpha = \lim_{\Delta t\to 0} \frac{\Delta \omega}{\Delta t} = \frac{d \omega}{dt} \qquad (\textnormal{Angular acceleration}) \tag{10.2} \end{equation} \begin{equation} \alpha = \frac{d}{dt} \frac{d \theta}{dt} = \frac{d^2 \theta}{dt^2} \end{equation} \begin{equation} \omega = \omega_0 + \alpha \, t \qquad (\textnormal{Angular velocity, constant angular acceleration}) \tag{10.3} \end{equation} \begin{equation} \Delta \theta = \frac{\omega_0 + \omega_f}{2} \, t \qquad (\textnormal{Angular displacement, constant angular acceleration}) \tag{10.4} \end{equation} \begin{equation} \theta = \theta_0 + \omega_0 \, t + \frac{1}{2} \alpha \, t^2 \qquad (\textnormal{Angular position}) \tag{10.5} \end{equation} \begin{equation} \omega^2 = \omega_0^2 + 2 \, \alpha \, \Delta \theta \qquad (\textnormal{Angular velocity}) \tag{10.6} \end{equation} \begin{equation} s = r \, \theta \qquad (\textnormal{Arc length}) \tag{10.7} \end{equation} \begin{equation} |\vec{\textbf{v}}_{tan}| = r \, \omega \qquad (\textnormal{Magnitude of tangential velocity}) \tag{10.8} \end{equation} \begin{equation} |\vec{\textbf{a}}_{tan}| = r \, \alpha \qquad (\textnormal{Magnitude of tangential acceleration}) \tag{10.9} \end{equation} \begin{equation} |\vec{\textbf{a}}_{rad}| = \frac{v^2}{R} = r \, \omega^2 \qquad (\textnormal{Magnitude of radial acceleration}) \tag{10.9} \end{equation} \begin{equation} I = m_1 r_1^2 + m_2 r_2^2 + \, ... \, = \sum_i m_i r_i^2 \qquad (\textnormal{Moment of inertia}) \tag{10.10} \end{equation} \begin{equation} K = \frac{1}{2} I \omega^2 \qquad (\textnormal{Rotational kinetic energy}) \tag{10.11} \end{equation} \begin{equation} I_p = I_{cm} + M d^2 \qquad (\textnormal{Parallel axis theorem}) \tag{10.12} \end{equation}
*** \begin{equation} I = \frac{2}{5} M R^2 \qquad (\textnormal{Moment of inertia of solid sphere}) \end{equation} \begin{equation} I = \frac{1}{12} M R^2 \qquad (\textnormal{Moment of inertia of rod through center}) \end{equation} \begin{equation} I = \frac{2}{3} M R^2 \qquad (\textnormal{Moment of inertia of hollow sphere}) \end{equation}
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