- #1
Warr
- 120
- 0
I have a question about the equation mechanics of cylindrical and spherical coordinate systems
This is basically about the velocity and acceleration equations of both
Let me just give an example from cylindrical
[tex]\vec v = \dot r\hat e_r + r\dot\theta\hat e_\theta + \dot z\hat k[/tex]
and
[tex]\vec a = (\ddot r - r\dot\theta^2)\hat e_r + (r\ddot\theta + 2\dot r\dot\theta)\hat e_\theta + \ddot z\hat k[/tex]
My question is, what is the physical meaning of [tex]\ddot r - r\dot\theta^2[/tex] if r is not changing. I thought that the coordinate system moved with the object you are measuring, and if so..how can there be an acceleration in the direction of [tex]\hat e_r[/tex] if [tex]\dot r = \ddot r = 0[/tex]
![Confused :confused: :confused:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
This is basically about the velocity and acceleration equations of both
Let me just give an example from cylindrical
[tex]\vec v = \dot r\hat e_r + r\dot\theta\hat e_\theta + \dot z\hat k[/tex]
and
[tex]\vec a = (\ddot r - r\dot\theta^2)\hat e_r + (r\ddot\theta + 2\dot r\dot\theta)\hat e_\theta + \ddot z\hat k[/tex]
My question is, what is the physical meaning of [tex]\ddot r - r\dot\theta^2[/tex] if r is not changing. I thought that the coordinate system moved with the object you are measuring, and if so..how can there be an acceleration in the direction of [tex]\hat e_r[/tex] if [tex]\dot r = \ddot r = 0[/tex]