# Rotation 2

Discipline
Materials

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We can think of two types of motion in this world:

• motion along a path (the Motion discipline), let’s call it linear motion, and
• motion around something, let’s call it rotational motion.

Forces cause linear motion. But what causes rotational motion? And how is rotation different from other motion?

This discipline fills in the final gaps and completes your understanding of motion and forces by adding their rotational versions. And it turns out to not be that hard; all formulas we found in the Motion and Forces disciplines have equivalent rotational versions. The only really new topics are about the connection between linear and rotational.

2nd of 2 courses in the Rotation discipline.
Meet the other participants in the Rotation classroom.

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

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