When we express acceleration in plane polar coordinates, we can find that $\vec{a}= \left(\ddot{r} - r \dot{\theta}^2\right)\hat{r} + \left(r \ddot{\theta}-2\dot{r}\dot{\theta}\right)\hat{\theta}$. Here, the first term indicates the radial acceleration and the second term indicates the centripetal acceleration.

Books say that the third term is the rate of change of tangential speed(?) and the fourth term is coriolis acceleration.

From the book 'Kleppner D., Kolenkow R.-An Introduction to Mechanics' From the book An Introduction to Mechanics by D. Kleppner and R. Kolenkow.

Now, the book says that the coriolis acceleration in our expression here is a real one.

Can anyone explain me the true meanings of the third and the fourth terms with physical interpretations ?

  • $\begingroup$ The third term is just the angular acceleration and the fourth one is the Coriolis acceleration, it's a real one here since our two direction vectors change with time. You've written the expression wrong in the start of your post. $\endgroup$
    – Rick
    Dec 2 '17 at 8:41
  • 2
    $\begingroup$ Possible duplicate of The two causes for the factor 2 in Coriolis effect $\endgroup$ Dec 2 '17 at 20:04
  • $\begingroup$ See answer here with diagram showing the directions and magnitudes of the changes in velocity (in polar form). All the terms above are explained graphically there. $\endgroup$ Dec 2 '17 at 20:05

The three most important accelerations are radial (d^2r/dt^2), centripetal (r*omega^2) (and angular (d^2-theta/dt^2). The least impactful is Coriolis.

Radial acceleration is like an explosion.

Centripetal acceleration is like David swinging a rock and killing Goliath.

Angular acceleration is turning on your Playstation 4 and playing Grand Theft Auto.

Coriolis acceleration is like shooting a projectile across a long distance on Earth and realizing that you miss your target when you're more than 2 miles away.