# Acceleration in plane polar coordinates [duplicate]

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 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 ?

• 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. – Rick Dec 2 '17 at 8:41
• Possible duplicate of The two causes for the factor 2 in Coriolis effect – John Alexiou Dec 2 '17 at 20:04
• 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. – John Alexiou Dec 2 '17 at 20:05