A Truck with 48-in diameter wheels is traveling at 50 miles/h.?

Question

a) Find the angular speed of the wheels in rad/min
b) How many revolutions per minute do the wheels make?

Answer 1

First, you need to convert the miles per hour into feet per minute and the diameter of the wheel also needs to be converted to feet (wheel diameter = 4 feet). To convert the 50 miles per hour to feet per minute you need to:

50 miles/hour = 50 mile/hour * 5280 feet/mile *1 hour/60 min

If you complete the calculation you will see that the units of mile and hour cancel each other out leaving only feet/min. So the numeric answer is 4400 feet/min.

Now the Speed (feet/min) = Angular speed (radians/min) * [Circumfence of wheel (feet) / (2 * PI *radians)]. The reason you divide the wheel circumfence by 2 * PI is that there are 2 * PI radians in a full circle. Also, you know Speed and you know the Circumfence of the wheel. So solving the equation for Angular speed gives Angular speed = 2200 radian/min which is the answer to part a).

To find the revolution per minute you need to do the following:

2200 radian/min = 2200 radian/min * [1 revolution / (2 * PI * radian)]. The units of radian will cancel each other out giving 2200 radian/min = 350.1 revolution/min or 350.1 RPM which is the answer to part b).

These type of problems are much easier when you carry your units throughout the problem. Carrying your units through the problem does not guarantee a correct answer. However, if your end answer is in the wrong units you can almost be sure that the numeric value is also wrong.
Hope this helps.

Answer 2

The distance travelled / hr=50 miles
. . . . . . . . " . . . . . . " . . ./ min = (50 x 8 x 220 x 3) / 60 feet
.. . . . . . . ." . . . . . . ." . . . . . = 4400 ft / min
48 inches = 4 feet; Radius = 4/2 = 2 feet
Circumference of the wheel = (2 x 22 x 2) / 7 feet
. . . . . . . " . . . . . . " . .. . . . . . .= 12.57 feet
The number of revolutions/min= Dist. / Circumference
. . . . . . . . . " . . . . . . . " . . .. . . = 4400 / 12.57
.................................................= 350.04 revolutios
=======================================
One revolution = 2 π radians
Hence, 350.04 x 2 π radians = 2200.25 radians/min
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Answer 3

properly.. the circumference of the wheel is: 2 x pi x 24 inches. (radius = diameter/2 = 24in) So, in 210 levels (it rather is 210/360 of an entire rotation of the wheel), the truck has long gone: 2 x pi x 24 x (210/360) inches. you're able to do the maths..

Answer 4

Part a)
v = ω r
ω = v / r
ω = (5280 x 50) / [ (60) (2) ] radians / min
ω = 5280 x 5/6 x 1/2 radians / min
ω = 2200 radians / min

Part b)
2π radians<------>1 rev
2200 radians<--> 2200 / 2π revs = 350 revs
Wheels make 350 revs / min

Answer 5

48 Inch Rims