r dot dot

Position:
\bf{ r } = r \hat r

Velocity:
\bf{ \dot r } = \dot r \hat r + \dot θ \hat θ


Acceleration:
\bf{ \ddot r }
= (\ddot r - r\dot θ^2) \hat r + (r\ddot θ + 2\dot r \dot θ) \hat θ
= roc of radial speed + centripetal acc. + angular acc. + coriolis acc.

Notes on acc.:
1. Each part has two terms.
2. Each terms has two dots. (because of the unit)
3. Each part has a `2'.
4. The 2nd term is negative. (centripetal)
5. Every term has an `r'. (because of the unit)
6. Every term except the 1st has a `θ'.
7. In each part, the front term depends on a \ddot.
8. In each part, the rear term depends on the angular speed.
9. The angular speed is more active than the \dot r.