SOLUTION: A car is moving at a rate of 79 miles per hour, and the diameter of its wheels is 1.8 feet. (Round your answers to three decimal places.)
(a) Find the number of revolutions pe
Question 1203146: A car is moving at a rate of 79 miles per hour, and the diameter of its wheels is 1.8 feet. (Round your answers to three decimal places.)
(a) Find the number of revolutions per minute the wheels are rotating.
revolutions per minute
(b) Find the angular speed of the wheels in radians per minute.
radians per minute Found 2 solutions by ikleyn, math_tutor2020:Answer by ikleyn(52781) (Show Source):
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A car is moving at a rate of 79 miles per hour, and the diameter of its wheels is 1.8 feet.
(Round your answers to three decimal places.)
(a) Find the number of revolutions per minute the wheels are rotating.
revolutions per minute
(b) Find the angular speed of the wheels in radians per minute.
radians per minute
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(a) is solved in three steps.
First step is to convert 79 miles per hour to feet per minute
79 miles per hour = feet per minute.
Second step is to write the circumference of the weel
circumference = = 3.14159*1.8 feet.
After that, the number of revolutions per minute is
the number of revolutions per minute = = 1229.358 (rounded). ANSWER
(b) 1229.358 revolutions per minute is = 2*3.14159*1229.358 = 7724.278 radians per minute (rounded). ANSWER
Solved.
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Three decimal is exceeding precision for such calculations.
Your input data is correct to one decimal place - so the result should be with one decimal place, not more.
Otherwise, calculations are not consistent with common sense.
circumference = pi*diameter
C = pi*d
C = pi*1.8
C = 1.8pi
1 revolution = 1.8pi feet
"miles" units cancel
"hours" units cancel
"feet" units cancel
After those cancellations, the only thing left will be "rev" up top and "min" down below
That gives the angular speed unit "revolutions per minute". This abbreviates to RPM.
The next step is to use a calculator, or scratch paper, to compute the following
This value is approximate. I used my calculator's stored version of pi to get the most accuracy possible.
After rounding to 3 decimal places.
This equation is valid only when the wheel diameter is 1.8 feet.
The approximate result is roughly 1229.384 rpm.
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Work Shown for part (b)
Refer to the previous part when we got to the step
I'll use that to avoid decimal rounding error.
"Rev" units cancel
The pi's cancel
This is approximate. The 4's go on forever.
After rounding to 3 decimal places.
Summary
79 mph = 1229.384 rpm
79 mph = 7724.444 radians per minute
Each decimal value is approximate.
This applies only when the wheel diameter is 1.8 feet.
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