Home > Courses > 1P21_Sternin > RotationalMotion Dynamics of extended bodies Torque = force $\times$ lever arm, $\tau=F \, l$ sign of $\tau$ = sense of rotation (+ve c.c.w.) lever arm = shortest distance to the line of force Equilibrium: $\sum \vec{F} = 0$ and $\sum \tau = 0$ provides another source of equations the point about which $\sum \tau = 0$ is arbitrary Center of gravity c.o.g. = the point about which total $\tau_{\rm weight}=0$ In problems involving weight: $\vec{W}$ acts on the body at c.o.g., and thus causes no torque about c.o.g. N2L for rotations $\tau = I \, \alpha, \quad \mbox{or} \quad \sum \tau = I_{\rm body} \alpha$ where the moment of inertia $I$ is a property of the extended body, determined by the spatial distribution of mass: $I=\sum_i m_i r_i^2$