\begin{equation} \vec{\boldsymbol{\tau}} = \vec{\textbf{r}} \times \vec{\textbf{F}} \qquad (\textnormal{Torque}) \tag{11.1} \end{equation} \begin{equation} \tau = I \alpha \qquad (\textnormal{Magnitude of torque}) \tag{11.2} \end{equation} \begin{equation} K = \frac{1}{2} M v_{cm}^2 + \frac{1}{2} I_{cm} \omega^2 \qquad (\textnormal{Rigid body with rotational and translation motion}) \tag{11.3} \end{equation} \begin{equation} v_{cm} = R \omega \qquad (\textnormal{Rolling without slipping}) \tag{11.4} \end{equation} \begin{equation} W = \int_{\theta_1}^{\theta_2} \tau \, d \theta \qquad (\textnormal{Work done by torque}) \tag{11.5} \end{equation} \begin{equation} W = \tau \Delta \theta \qquad (\textnormal{Work done by constant torque}) \tag{11.6} \end{equation} \begin{equation} W_{ext} = \int_{\omega_1}^{\omega_2} I \omega \, d \omega = \frac{1}{2} I (\omega_2^2 - \omega_1^2) \qquad (\textnormal{Work}) \tag{11.7} \end{equation} \begin{equation} P = \tau \omega \qquad (\textnormal{Power}) \tag{11.8} \end{equation} \begin{equation} \vec{\textbf{L}} = \vec{\textbf{r}} \times \vec{\textbf{p}} = \vec{\textbf{r}} \times m \,\vec{\textbf{v}} \qquad (\textnormal{Angular momentum}) \tag{11.9} \end{equation} \begin{equation} \vec{\textbf{L}} = I \vec{\boldsymbol{\omega}} \qquad (\textnormal{Rigid body rotating around symmetry axis}) \tag{11.10} \end{equation} \begin{equation} \vec{\boldsymbol{\tau}} = \frac{d \vec{\textbf{L}}}{dt} \qquad (\textnormal{For a system of particles}) \tag{11.11} \end{equation}
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