Velocity from position vector in rotating object

AI Thread Summary
The discussion revolves around calculating the change in velocity for the center of a tire rim in relation to its contact patch, particularly considering camber effects. The user has successfully derived the position vector but is confused about the derivation of certain terms in their equation, specifically the use of the unit vector i in relation to the yaw moment and the implications of the fourth term involving dk/dt. There is a request for clarification on the mathematical reasoning behind these terms, indicating a need for more visual context to aid understanding. The conversation highlights the importance of clear notation and figures in solving complex physics problems. Overall, the thread emphasizes the challenges of deriving equations in rotational dynamics and the necessity for collaborative clarification.
Nikstykal
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Q1.PNG

Homework Statement


I am trying to solve for change in velocity for the center of a rim with respect to the contact patch of a tire that has some degree of camber. The equation finalized is shown in the image below, equation 2.6.
http://imgur.com/a/oHucp

Homework Equations

The Attempt at a Solution


I understand how to get the position vector shown in 2.5. The first part of 2.6 is just deriving 2.5 with respect to h. The 3rd and 4th terms are what confuse me. In regards to dj/dt = -wz i, I understand that the change in j with respect to time is directly related to the yaw moment (wz) but what is the mathematical reasoning for using the i unit vector? Further, the 4th term demonstrates that dk/dt = -γ' / cos2 γ j, showing that k = -tanγ.
Sorry for the improper notation, was hoping to get further insight into how these terms are being derived.
 
Last edited:
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I can't see your figure, and without that, there is no good way to reply to you. Please get the figure into the post.
 
Dr.D said:
I can't see your figure, and without that, there is no good way to reply to you. Please get the figure into the post.
Sorry about that, should be fixed.
 

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