Question 1208203
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Tutor Edwin arrived at the correct revolutions per minute (rpm) value, which was {{{1650/pi}}}


However, he made an error when computing the "83.6 radians per minute" value. 
Instead of dividing, multiply {{{1650/pi}}} with {{{2pi}}}


You may be asking "how do I know whether to multiply or divide by 2pi?"
One way to remember is to set something up like this
{{{
(matrix(1,2,1650,"revolutions")/matrix(1,2,pi,"minutes"))
(matrix(1,2,2pi,"radians")/matrix(1,2,1,"revolution"))
=
matrix(1,4,3300,"radians","per","minute") 
}}}
The "revolutions" units cancel out. So do the pi terms.


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Here is how I would compute the revolutions per minute (rpm) value
{{{ 
(matrix(1,2,50,"miles")/matrix(1,2,1,"hour"))
(matrix(1,2,1,"hour")/matrix(1,2,60,"min"))
(matrix(1,2,5280,"feet")/matrix(1,2,1,"mile"))
(matrix(1,2,12,"inches")/matrix(1,2,1,"foot"))
(matrix(1,2,1,"revolution")/matrix(1,2,32pi,"inches"))
=
matrix(1,4,1650/pi,"revolutions","per","minute")
}}}
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.


{{{1650/pi = 525.211312}}} approximately
I used the calculator's stored version of pi to get the most accuracy possible.


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If you wanted to use a similar template to find the radians per minute value, then,
{{{
highlight_green(
(matrix(1,2,50,"miles")/matrix(1,2,1,"hour"))
(matrix(1,2,1,"hour")/matrix(1,2,60,"min"))
(matrix(1,2,5280,"feet")/matrix(1,2,1,"mile"))
(matrix(1,2,12,"inches")/matrix(1,2,1,"foot"))
(matrix(1,2,1,"revolution")/matrix(1,2,32pi,"inches")))
(matrix(1,2,2pi,"radians")/matrix(1,2,1,"revolution"))
=
highlight_green((matrix(1,2,1650,"revolutions")/matrix(1,2,pi,"minutes")))
(matrix(1,2,2pi,"radians")/matrix(1,2,1,"revolution"))
=
matrix(1,4,3300,"radians","per","minute")
}}}
The pi terms cancel, along with nearly every unit except for the "radians" up top and "minutes" down below.
The stuff in green is the calculation in the previous section.


Side note: it's unfortunate that both "revolutions" and "radians" start with R.
For new students it might be easy to mistake "rpm" to mean "radians per minute"


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Answers: 
Radians per minute = <font color=red>3300</font>
Revolutions per minute (rpm) = <font color=red>1650/pi = 525.211312 (approximate)</font>
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