I Significance of terms of acceleration in polar coordinates

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1. Mar 22, 2017

Mind----Blown

How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction?

from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ;

(where er and eθ are unit vectors in the radial direction and the direction of increase of the polar angle, θ.)

The two components in er direction--- r¨ and rθ˙^2 are the usual acceleration along radius vector and the centrifugal force experienced. But what is the significance of the other two terms?. Is there any day-to-day or a common situation where we experience the Coriolis force and the other term?

I can memorize the formula and use it, but i will truly 'understand' its significance only if i can 'feel' the terms..

Thanks!

2. Mar 22, 2017

ZapperZ

Staff Emeritus
Here's what you can do, and it is a step-by-step "addition of complications":

1. Start with something you know. What does the equation looks like if you have a uniform circular motion, i.e. r=constant, and dθ/dt = constant?

2. Now, add the case where dθ/dt is not a constant, i.e. the object is still at the same radius, but the rate of it spinning around the axis is changing. What terms survive now?

3. Now what if dr/dt is not zero, but a constant? The object is now having not only a changing rate of spin, but also it is changing its distance from the axis at a constant rate. Which terms survive?

4. Finally, what if the radial acceleration is not zero, i.e. dr/dt is no longer a constant?

You start with something you know of conceptually, and then you start loosening the constraints. Each of the term that starts to survive is related to the constraints. Try it. See if this helps you to have a physical understanding of what each of those terms represents.

Zz.

3. Mar 22, 2017

Staff: Mentor

You and a friend or two should go to a park, get on a merry go round, and throw a ball to each other. That will certainly help you "feel" the terms in a visceral manner.

Last edited: Mar 22, 2017
4. Mar 23, 2017

Staff: Mentor

Also, get on the merry go round closer to the axis than he is, and walk toward your friend.