On the Kinematics Exercise handout due for Wednesday 08/29, for position 1, I have doubts on how to establish the positions of e_r and e_theta. I know they both go in the positive r and theta directions, so my guess in position 1 for e_r is that it points opposite observer O (since r is decreasing) and e_theta is perpendicular to e_r and pointing towards the inside of the path (the picture above shows both). I am really not sure about this though... Any comments?
3 comments:
The direction that you have shown for e_r is correct: e_r always points outward from the observer toward the point of interest P (regardless of how the point moves.
e_theta is perpendicular to e_r; it points in the direction of "increasing theta" (regardless of how point P moves). Actually, your e_theta should point the other way since increasing theta has line OP rotating CW; however, it does not affect anything here since you are not finding theta_dot.
You have information about the coordinates of point P. You can use the coordinates to find the angle theta. With that, e_r = cos(theta)*i - sin(theta)*j .
Let me know if I have not answered your question.
Don't we also need e_theta in terms of i and j to find r_dot? I calculated theta, but I don't see how to get r_dot by just using e_r.
Don't we also consider e_theta term (r*theta_dot) to relate this to a given velocity vector?
JJ,
You are correct -- you need to find both e_r and e_theta to get r_dot. My comment above implies otherwise.
My point was that if you get the direction wrong with e_theta it will affect the only the sign on theta_dot and it will not affect the answer for r_dot.
Thanks for pointing out this.
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