Hi Dany Spencer Adams,<\/p>\n
I think there might be an error in the equation for converting RCF to rpm on page 140 of the second edition, hardcover.<\/p>\n
Should the equation be:<\/p>\n
rpm<\/i>= (RCF \/ (r<\/i> x 1.118 x 10^-6<\/b>))^1\/2<\/p>\n
instead of 10^-5?<\/p>\n
because the radius is measured in mm?<\/p>\n
\u2026
\nE. D.<\/p>\n
Dear E. D.<\/p>\n
Thank you for pointing out the issue. \u00a0You are correct.\u00a0 The difference has to do with the units of radius.<\/p>\n
If you look around, you will find that there is no convention for whether to report the radius of the rotor in mm or cm. \u00a0Unfortunately, I didn\u2019t make it clear that there are two versions in common use, and that they are both in the book specifically to show that. \u00a0On page 139, it is written out correctly for mm, and it states explicitly that I mean radius in mm. \u00a0On page 140, I switched to cm, with only a parenthetical comment that I had done that. \u00a0I really should make that more obvious. \u00a0When using cm, the exponent is \u20135, when using mm the exponent is \u20136.<\/p>\n
One way to think about it is to imagine measuring the rotor in mm, now imagine measuring the exact same rotor in cm. \u00a0The second measurement is going to be the first measurement divided by 10. \u00a0But the RCF hasn\u2019t changed. \u00a0To take that \u201cdivide by 10\u201d into account, therefore, you need to multiply the answer by 10, or you won\u2019t get the same RCF. \u00a0That \u201cmultiply by 10\u201d gets folded into the constant so the exponent becomes 10^-5.<\/p>\n","protected":false},"excerpt":{"rendered":"
Hi Dany Spencer Adams, I think there might be an error in the equation for converting RCF to rpm on page 140 of the second edition, hardcover. Should the equation be: rpm= (RCF \/ (r x 1.118 x 10^-6))^1\/2 instead of 10^-5? because the radius is measured in mm? \u2026 E. D. Dear E. D. […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts\/600"}],"collection":[{"href":"https:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=600"}],"version-history":[{"count":3,"href":"https:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts\/600\/revisions"}],"predecessor-version":[{"id":604,"href":"https:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts\/600\/revisions\/604"}],"wp:attachment":[{"href":"https:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}