Welcome to the website of ME 274 for the Fall 2008 semester. On this site you can view blog posts, add your own blog posts and add comments to existing posts. In addition to the blog are links to course material:
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Comments and suggestions:
4 comments:
I'm working on 7/21 and I've got about two full lines worth of i's, j's and k's from cross products using r_B/O. Is there a simpler way to do this or is there simply some complicated cross products involved with these problems?
-Adam Watson
When we're using the relative motion equations, I'm slightly confused why we can use a_O and v_O as reference points. I'm not sure of the connection we can make between these fixed origin points and where we put the observer. The observer is not attached to O so why would (v_P/O)rel and (a_P/O)rel be the same as the relative 'v' and 'a' seen by the observer?
-Sheng Yang
--Adam--
Unfortunately, there are no short cuts that one can take in doing these products. One must work through all of the terms as they appear.
In general, both r and omega can have three components each. In that case, omega x r will have up to six non-zero terms, and omega x (omega x r) can then have up to 24 terms. So if its any consolation, it could be worse...
Good question.
--Sheng--
The conditions that are placed on the choice of point O is that it must be on the same rigid body as the observer. In both of these problems point O actually is on the same rigid body as the observer chosen. Recall that the definition of a rigid body is that the distance between any two points of the body must remain constant as the body moves. For 7/10, the distance between O and P remains constant, as well as the distance between O and B remains constant for 7/21.
One way to check this out is to imagination yourself as the observer. If O is on the same rigid body as you the observer, O will not appear to move from your vantage point. This test works for both of these problems.
Let me know if this is not clear.
This is an excellent fundamental question. Thanks for asking!
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