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.

*1st 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 |