Wednesday, August 29, 2007
Homework Question 5/12 Question
I understand that there is no k term in the velocity because it is canceled during the cross product. However, I don't understand why there is not a k term in the acceleration of P since there is the final radius term where you simply multiply it by omega squared. Shouldn't this carry over to the final answer because that is not what you got on the video solution.
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This is a good question. Let me give you first a quick answer, and then follow it up with a more in-depth answer.
* Note that the motion of point P is the same as the motion of the point immediately below P on the arm (call that point A). The paths of P and A are the same, only the path of A is 50 mm below that of P. I have effectively found the acceleration of A in the video solution with the understanding that it is the same as P.
* Now for a longer, a more complete, answer. The form of the equation developed in class has -omega^2*rP/O as the third term on the RHS. This equation is valid for two points O and P that lie in the same plane. In this problem, it is valid for O and A. The more complete form of the equation, and one that appears in the textbook, has the third term written as omega x (omega x rP/O). This equation is valid even if P and O are not in the same plane. If you use this equation on this problem, you will find the same result as I got in the video solution.
All problems in Chapter 5 that we will solve in this course (except Problem 5/12 !) has all points lying in the same plane. Bad luck for me that the very first problem that I work is the one exception!
I will try to cover this point in class on Friday. If I forget, don't be shy to remind me.
Thanks for bringing this to my attention.
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