document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208203>Question 1208203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car is moving at a rate of 50 miles per hour with a wheel radius of 16 inches, find the Angular speed in radians per minute and the number of revolutions per minute </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846470 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Tutor Edwin arrived at the correct revolutions per minute (rpm) value, which was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1650%2Fpi ALIGN=MIDDLE  ALT=\"1650%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, he made an error when computing the \"83.6 radians per minute\" value. <BR>\n" );
document.write( "Instead of dividing, multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1650%2Fpi ALIGN=MIDDLE  ALT=\"1650%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You may be asking \"how do I know whether to multiply or divide by 2pi?\"<BR>\n" );
document.write( "One way to remember is to set something up like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C1650%2C%22revolutions%22%29%2Fmatrix%281%2C2%2Cpi%2C%22minutes%22%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22radians%22%29%2Fmatrix%281%2C2%2C1%2C%22revolution%22%29%29%0D%0A=%0D%0Amatrix%281%2C4%2C3300%2C%22radians%22%2C%22per%22%2C%22minute%22%29+%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The \"revolutions\" units cancel out. So do the pi terms.\r<BR>\n" );
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document.write( "Here is how I would compute the revolutions per minute (rpm) value<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%0D%0A%28matrix%281%2C2%2C50%2C%22miles%22%29%2Fmatrix%281%2C2%2C1%2C%22hour%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22hour%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22feet%22%29%2Fmatrix%281%2C2%2C1%2C%22mile%22%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22inches%22%29%2Fmatrix%281%2C2%2C1%2C%22foot%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22revolution%22%29%2Fmatrix%281%2C2%2C32pi%2C%22inches%22%29%29%0D%0A=%0D%0Amatrix%281%2C4%2C1650%2Fpi%2C%22revolutions%22%2C%22per%22%2C%22minute%22%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each conversion factor is based on these facts<ul><li>1 hour = 60 min</li><li>5280 feet = 1 mile</li><li>12 inches = 1 foot</li><li>1 revolution = 32pi inches of circumference (since circumference = 2*pi*radius = 2*pi*16 = 32pi)</li></ul>Nearly every unit cancels except for the \"revolutions\" up top and \"minutes\" down below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1650%2Fpi+=+525.211312 ALIGN=MIDDLE  ALT=\"1650%2Fpi+=+525.211312\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately<BR>\n" );
document.write( "I used the calculator's stored version of pi to get the most accuracy possible.\r<BR>\n" );
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document.write( "If you wanted to use a similar template to find the radians per minute value, then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Ahighlight_green%28%0D%0A%28matrix%281%2C2%2C50%2C%22miles%22%29%2Fmatrix%281%2C2%2C1%2C%22hour%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22hour%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22feet%22%29%2Fmatrix%281%2C2%2C1%2C%22mile%22%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22inches%22%29%2Fmatrix%281%2C2%2C1%2C%22foot%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22revolution%22%29%2Fmatrix%281%2C2%2C32pi%2C%22inches%22%29%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22radians%22%29%2Fmatrix%281%2C2%2C1%2C%22revolution%22%29%29%0D%0A=%0D%0Ahighlight_green%28%28matrix%281%2C2%2C1650%2C%22revolutions%22%29%2Fmatrix%281%2C2%2Cpi%2C%22minutes%22%29%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22radians%22%29%2Fmatrix%281%2C2%2C1%2C%22revolution%22%29%29%0D%0A=%0D%0Amatrix%281%2C4%2C3300%2C%22radians%22%2C%22per%22%2C%22minute%22%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The pi terms cancel, along with nearly every unit except for the \"radians\" up top and \"minutes\" down below.<BR>\n" );
document.write( "The stuff in green is the calculation in the previous section.\r<BR>\n" );
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document.write( "Side note: it's unfortunate that both \"revolutions\" and \"radians\" start with R.<BR>\n" );
document.write( "For new students it might be easy to mistake \"rpm\" to mean \"radians per minute\"\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "Radians per minute = <font color=red>3300</font><BR>\n" );
document.write( "Revolutions per minute (rpm) = <font color=red>1650/pi = 525.211312 (approximate)</font><BR>\n" );
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