document.write( "Question 242004: please help me solve this problem:
\n" ); document.write( "A wheel turns 1,500 revolutions per minute.How fast does it turn in radians per second?
\n" ); document.write( "HERE ARE THE POSSIBLE ANSWERS:
\n" ); document.write( "a)15pi rad/sec
\n" ); document.write( "b)30pi rad/sec
\n" ); document.write( "c)300pi rad/sec \n" ); document.write( "

Algebra.Com's Answer #177187 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
The basic problem is to convert revolutions to radians and minutes to seconds. One complete revolution is $\"2pi\"$ radians. And 1 minute equals 60 seconds.

\n" ); document.write( "When converting units like this, if you are unsure of whether to multiply or divide, you can use what I call unit Algebra to help. Just make a fraction of your conversions and include the units. There will two ways to make these fractions depending on which unit you decide to put on top. Here are the possibel fractions for this problem:
\n" ); document.write( "

\r\n" );
document.write( " 1 revolution\r\n" );
document.write( "________________\r\n" );
document.write( "radians\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "radians\r\n" );
document.write( "__________________\r\n" );
document.write( "  1 revolution\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "  1 minute\r\n" );
document.write( "____________\r\n" );
document.write( " 60 seconds\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 60 seconds\r\n" );
document.write( "____________\r\n" );
document.write( "  1 minute\r\n" );
document.write( "

\n" ); document.write( "The tough part of this is understanding that all these fractions are 1's!! Although the numbers in the numerators and denominators are not the same as we would usually expect in a fraction that equals one, the numerators and denominators are equal. After all, isn't 1 minute the same amount of time as 60 seconds?

\n" ); document.write( "Now we just figure out which of the fractions to use. What we will be doing is multiplying
\n" ); document.write( "

\r\n" );
document.write( "1500 revolutions\r\n" );
document.write( "________________\r\n" );
document.write( "1 minute\r\n" );
document.write( "

\n" ); document.write( "by two of these fractions and, since multiplying by 1's (no matter how weird they look) does not change the number, we will be able to get the answer we want.

\n" ); document.write( "Let's try
\n" ); document.write( "

\r\n" );
document.write( "1500 revolutions     1 revolution       60 seconds  \r\n" );
document.write( "________________  * _________________ * __________\r\n" );
document.write( "1 minute            radians          1 minute\r\n" );
document.write( "

\n" ); document.write( "We want an answer that is radians/second. So we want the minutes and revolutions to disappear. We want them to cancel. But with the expression above, \"revolution\" is in 2 numerators and no denominators. So they will not cancel. Similarly the \"minutes\" are in 2 denominators but no numerators. So they do not cancel either. We want \"revolutions\" and \"minutes\" to appear in the numerator and denominator the same number of times so they all cancel out.

\n" ); document.write( "Let's see how the correct choice of fractions looks:
\n" ); document.write( "

\r\n" );
document.write( "1500 revolutions    radians          1 minute\r\n" );
document.write( "________________ *  _________________ * ___________\r\n" );
document.write( "  1 minute           1 revolution       60 seconds\r\n" );
document.write( "

\n" ); document.write( "\"revolutions\" and \"minutes\" each appear once in the numerator and once in the denominator. So they will cancel out. The units that will remain are \"radians\" in the numerator and \"seconds\" in the denominator which is exactly what we are looking for. After canceling the \"revolutions\" and \"minutes\" we are left with:
\n" ); document.write( "

\r\n" );
document.write( " 1500      radians              1\r\n" );
document.write( " ____  *   _________________ * ____________\r\n" );
document.write( "   1             1              60 seconds\r\n" );
document.write( "

\n" ); document.write( "Since 1500/60 = 25 this simplifies to:
\n" ); document.write( "

\r\n" );
document.write( " 25*radians\r\n" );
document.write( "____________________\r\n" );
document.write( "    1 second\r\n" );
document.write( "

\n" ); document.write( "which simplifies to
\n" ); document.write( "

\r\n" );
document.write( "radians\r\n" );
document.write( "____________________\r\n" );
document.write( "    1 second\r\n" );
document.write( "

\n" ); document.write( "Although this does not match any of the answers you provided, it is the correct answer for the problem you described. \n" ); document.write( "

\n" );