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# Summary of Rotation 1

You have finished the 1st half of Rotation! We have been through the unblurred points in the lists below. Continue to to complete the Rotation discipline.

All learned properties and mechanisms are stored as memories on your profile, where you can always go to brush them up. If you struggle with any topics in the tests, the Existence classroom is a great place to seek aid.

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