[[Torque and Rotational Dynamics]] # Summary * Angular displacement is measured with $\Delta \theta=\theta-\theta_0$ * Track angular displacement direction with clockwise counterclockwise sign convention * Average angular velocity: $w_{avg}=\frac{\Delta\theta}{\Delta t}$ * Average angular acceleration: $a_{avg}=\frac{\Delta w}{\Delta t}$ * Rigid system holds shape, but different parts move at different speeds so you can't treat it as a single particle unless COM motion describes rotation well * Slope of theta vs time shows angular velocity * Slope of angular velocity vs time shows angular acceleration * Integral of angular velocity vs time shows Delta theta # Angular vs. Linear Motion Angular motion equations are similar to linear motion equations. $w=w_0+at$ $\theta=\theta_0+w_0t+\frac{1}{2}at^2$ $w^2=w^2_0+2a(\theta - \theta_0)$