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Hi all,<BR>
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I always caution my students that friction is a very complex topic. If you do a web search and look at research details on friction, you find out more and more factors that need to be included... This morning in a brief search, I found <BR>
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<A href="http://www.school-for-champions.com/science/friction_rolling.htm">http://www.school-for-champions.com/science/friction_rolling.htm</A> does a good job of discussing hard versus soft wheels and surfaces. <BR>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-FAMILY: Arial; FONT-SIZE: 10pt"><A href="http://books.google.com/books?id=Qc6ISmqcnyAC&pg=PA249&lpg=PA249&dq=rolling+friction+torque&source=bl&ots=T5C0awX_C_&sig=YFo64pWig_ZXxuFK_CiVDnOytU0&hl=en&ei=Xo7qS4_yAoKC8gaxwpnlDg&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEQQ6AEwBw#v=onepage&q=rolling%20friction%20torque&f=false"><FONT color=#0000ff>http://books.google.com/books?id=Qc6ISmqcnyAC&pg=PA249&lpg=PA249&dq=rolling+friction+torque&source=bl&ots=T5C0awX_C_&sig=YFo64pWig_ZXxuFK_CiVDnOytU0&hl=en&ei=Xo7qS4_yAoKC8gaxwpnlDg&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEQQ6AEwBw#v=onepage&q=rolling%20friction%20torque&f=false</FONT></A><o:p></o:p></SPAN></P>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-FAMILY: Arial; FONT-SIZE: 10pt">is an excerpt from an engineering book that adds more details to the spherical cow….the author indicates 8 identified factors in the frictional torque of a roller bearing in a track: differential slip, gyroscopic spin, elastic hysteresis of the materials, microroughness of the materials and lack of geometric symmetry, rubbing on the housing(which probably doesn't address Mike's question), shearing of the lubricant, air resistance, and a temperature factor. Even with all of these it is interesting to note that a final factor, K-alludes to other unaccounted for, but partially listed forces, acknowledging the cow still needs more detail.</SPAN></P>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-FAMILY: Arial; FONT-SIZE: 10pt"><o:p>Not sure how much of this is relevant to Mike's vector question, but it does again emphasize that analysis of real systems relies on approximations that approach reality.</o:p></SPAN></P>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal><?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" /><st1:City><st1:place><SPAN style="FONT-FAMILY: Arial; FONT-SIZE: 10pt">Roy</SPAN></st1:place></st1:City><SPAN style="FONT-FAMILY: Arial; FONT-SIZE: 10pt"> <o:p></o:p></SPAN></P>
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