SOLUTION: A truck with 48-in.-diameter wheels is traveling at 50 mi/h. a.) Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes: b

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Question 1203363: A truck with 48-in.-diameter wheels is traveling at 50 mi/h.
a.) Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes:
b.) How many revolutions per minute do the wheels make?

Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
A truck with 48-in.-diameter wheels is traveling at 50 mi/h.
a.) Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes:
b.) How many revolutions per minute do the wheels make?
~~~~~~~~~~~~~~~~~

1 mile = 5280 feet = 5280*12 inches = 63360 inches.


The wheel circumference is pi%2A48 inches = 3.14159265*48 inches = 150.7964472 inches.


The number of revolutions of the wheel per minute is  rpm = %28%28%2863360%2A50%29%2F60%29%29%2F150.7964472 = 350.1408752.


The angular velocity = 2%2Api%2Arpm = 2%2A3.14159265%2A350.1408752 = 2200 radians per minute.

Solved.

The formulas are self-explanatory.

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Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1 hour = 60 min
5280 feet = 1 mile
12 inches = 1 ft
1 revolution = 48pi inches
2pi radians = 1 revolution

The 48pi refers to the circumference of the circle of diameter 48 inches.
C = pi*diameter

Each of those equivalences then form a fraction as shown in this long conversion string

The placement of each item is to form the next set of cancellations as I'll describe below.

"miles" units cancel

"hours" units cancel

"feet" units cancel

"inches" units cancel

"revolution" units cancel

There's a lot of cancellations going on.
After the dust settles, we have "radians" up top and "minutes" in the bottom.
Those are the only two units left.

Multiply the values along the top: 50*1*5280*12*2pi = 6,336,000pi

Multiply the values along the bottom: 1*60*1*1*48pi*1 = 2880pi

We end up with %286336000pi%29%2F%282880pi%29+=+2200

Answer to part (a) is 2200 radians per minute

=======================================================

Part (b)

We'll have this conversion string

The key difference is we don't involve "2pi radians = 1 rev" at the very end.

So we haven't multiplied by 2pi. We can divide the previous result 2200 rad/min by 2pi to get the rpm (revolutions per min)

rpm = (rads per min)/(2pi)
rpm = (2200)/(2pi)
rpm = 350.14087480217 approximately

I used the calculator's stored version of pi to get the most accuracy possible.
If your teacher instructs you to use something like pi = 3.14, then be sure to do so. Round the final answer however your teacher instructs.