I REALLY NEED HELP!!!!!!!!!!
A truck with 32-in.-diameter wheels is traveling at 60 mi/h. Find the angular speed of
the wheels in rad/min. How many revolutions per minute do the wheels make?

- anonymous

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- anonymous

does any1 know how to do this?

- anonymous

?

- jdoe0001

heheh

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## More answers

- anonymous

u know what i mean
any way do u know how t do this problem?

- jdoe0001

the truck is going 60 miles per hour
how many inches would that be? well
keep in mind there are 5250 feet in 1 mile, and 12 inches per foot
\(\bf 60\ miles \implies (60 \times 5280) ft = 316800\\
\textit{how many inches? well, }316800 \times 12 = 3801600\\
\textit{so there are 3801600 inches in 60 miles}\)

- jdoe0001

so the truck is really going at 3801600 miles per hour
well, what's that in minutes? well, there are 60 minutes per hour, so 3801600/60
well, how many is that in seconds? well, since there are 60 secs per minute it'd be THAT AMOUNT divided by 60

- anonymous

wait isnt it 3801600 inches per hr?

- jdoe0001

ohh shoot, yes, inches per hour indeed

- jdoe0001

right, we were converting to inches 60 * 5280 * 12

- jdoe0001

and so, how many inches is the truck going per second?
well \(\bf \cfrac{3801600}{60(mins)} = 63360 \qquad \qquad \cfrac{63360}{60(secs)} = 1056\)

- jdoe0001

so we can say that the truck is really going at 1056 inches per second
actually we don't need the secs unit, just the minute

- jdoe0001

so the truck is going at 63360 inches per minute

- anonymous

so we want 63360 in/ min?

- anonymous

is the radians the inches?

- jdoe0001

so now let's take a peek at the wheel
the diameter is 32 inches long
that means the radius is half that, 16 inches
so we want to know the circumference of the wheel|dw:1377550085206:dw|

- jdoe0001

radians is the angular unit

- jdoe0001

when asked on "angular speed" all they're really asking is "how many angles per time unit are there"

- jdoe0001

in this case is just " how many angles per minute is the truck going"

- anonymous

angles per minute?

- jdoe0001

well, heehhe, radians in this case, but yes, I gather angles might sound more something you may know

- anonymous

ohh i understand

- jdoe0001

you know what a geometric angle is right? just the opening between two lines

- anonymous

ya

- jdoe0001

and to get that, we need to know from the point a spot on the whee touches the road and goes around, till the point it gets back again to the same point
that is the circumference
|dw:1377550450904:dw|

- jdoe0001

that will tell us, how far the truck goes on one "go around" of the wheel

- anonymous

so its 100.531

- jdoe0001

yes it s 100.531
so we can say that in one "go around" of the wheel, the truck is only doing 100.531 inches
well, how many radians is that? well, one "go around" is \(\large 2\pi\)
so we can say that the amount of radians done in 1 minute is => \(\bf \cfrac{100.53}{2 \pi}\)

- anonymous

so 157.914

- jdoe0001

well, \(\bf \cfrac{100.53}{2 \pi} = 157.9 \ radians\)

- anonymous

so thats the rad/min?

- anonymous

or the revolutions/min?

- jdoe0001

can't be radians, since it's inches over radians, the \(2\pi\) is the radian unit already, thus \(\bf \cfrac{100.53in}{2 \pi}\)

- anonymous

so its revolutions

- jdoe0001

hmmm gimme a sec

- anonymous

ok

- jdoe0001

\(\bf \textit{is going at 100.53in per revolution}\\
63360\ in/min\\
\cfrac{63360 \frac{in}{min}}{100.53 in} \implies \cfrac{63360in}{min}\times \cfrac{1}{100.53in} \implies 63360min\)

- jdoe0001

hmmm well, so much for much typing

- jdoe0001

\(\bf \textit{is going at 100.53in per revolution}\\
63360\ in/min\\
\cfrac{63360 \frac{in}{min}}{100.53 in} \implies \cfrac{63360in}{min}\times \cfrac{1}{100.53in} \implies 630.25min\) rather

- jdoe0001

the angular speed will be angle/time, thus that is 630.25 per each revolution
since we were using the circumference value of 100.53 which is 2pi

- anonymous

so whats the rad/min?

- jdoe0001

so the speed will end up as \(\bf \cfrac{2\pi}{630.25}\\
\textit{dividing both sides by } 2 \pi\\
\cfrac{1}{\frac{630.25}{2\pi}}\)
to get the value for 1 radian per min

- jdoe0001

hmm so the value per radian ends up as 100.53 rad/min

- jdoe0001

lemme recheck myself

- anonymous

so thats the answer?

- anonymous

kk

- jdoe0001

no.... can't be
if the circumference is 100.53 inches long
how many radians does it do? well, dividing that by 2pi I get 16
so it does 16 inches per radians
and we have 63360 inches in one minute
so the amount of radians is, just the equivalence of it in inches, and dividing
\(\bf \cfrac{63360\frac{in}{min}}{16\frac{in}{rad}} \implies \cfrac{63360 in}{min} \times \cfrac{rad}{16in}\implies 3960 \cfrac{rad}{min}\)

- jdoe0001

the revolutions are easy since we already have the amount of inches it does per 2pi and per min
so just dividing 63360/100.53 will give 630.25 revolutions per minute

- anonymous

k...and the radians per min are 100.531rad/min

- jdoe0001

3960 rad/min
you see the circumference is 100.53 which is 2pi
to know how many inches per radian, we divide 100.53, and get 16
thus we know there are 16 inches for each radian
then as above, we divide the radian = 16 inches
by
63360 inches

- jdoe0001

so we're converting the circumference from inches to rad
then using the radian value to divide the in/min the truck wheel does

- anonymous

thx so much

- jdoe0001

yw

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