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# Summary of Rotation

You have completed the Rotation discipline! We’d recommend that you continue to the Interaction discipline, starting with .

All learned properties and mechanisms are stored as memories on your profile, where you can always go to brush them up. Don’t forget the Motion classroom for aid, questions and guidance while doing the finishing tasks.

New properties
Angular position$\vec \theta$
Angular velocity$\vec \omega$
Angular acceleration$\vec \alpha$
Torque$\vec \tau$
Moment-of-inertia$I$
New mechanisms
Definitions$$\vec \omega=\vec \theta'$$
$$\vec \alpha=\vec \omega'$$
$$\vec \tau=\vec r \times \vec F$$
$$I=\sum mr^2$$
Angular motion equations$$\omega=\omega_0+\alpha t$$
$$\theta=\theta_0+\omega_0t+\frac12\alpha t^2$$
$$\omega^2=\omega_0^2+2\alpha (\theta-\theta_0)$$
$$\theta=\theta_0+\frac12(\omega+\omega_0)t$$
Newton's 1st and 2nd law in rotation$$\sum\vec \tau=0$$
$$\sum\vec \tau=I\vec\alpha$$
Parallel-axis theorem$$I=I_\text{com}+md^2$$
New phenomena
Geometric bonds$$s=r\theta$$
$$v=r\omega$$
$$a=r\alpha$$
Centre-of-mass$$\vec r_\text{com}=\frac{\sum m\vec r}{\sum m}$$
Rolling
Pulleys