A tire .762m in radius rotates at a constant rate of 122rev/min. Find the speed of a stone in the tread oftire

Question

radius is .762 meters
speed is 122 revolutions per minute
find speed of stone lodged in tire

Answer 1

This is a simple conversion problem. You want to convert radians per second to meters per second or to miles per hour.

Here is how to do it:

122 rev / min x 1 min / 60s x 6.28radians / 1 revolution x 0.762m / 1radian = 583.8m / 60s = 9.73m/s

If you write all of this out so that the fractions are vertical rather than horizontal you can see how all of the units cancel each other leaving you with meters on top and seconds on bottom.

Now, if you want your answer in miles per hour here is how to do that conversion:

9.73m / s x 1 mile / 1609m x 3600s / hour = 35028.84mi / 1609hr = 21.7mph.

Now that you see the full answer here is a short version.

Whenever you want to convert revolutions per minute to meters per second you will always have the meters to radians conversion, the radians to revolutions conversion and the minutes to second conversion. All of these can be done with one calculation rather than three:
The number of rev/min x radius (in meters) x 0.1047 = speed in m/s

To convert m/s to mph just multiply the number of m/s by 2.24 and you will get miles per hour.

Answer 2

Find the circumference of the tire, first. C=(pi)*d (diameter is twice the radius).

Then, you can multiply that by the number of times it goes around in a minute. You will have the speed of the stone in m/min. Multiply by 60 to find m/s.

Answer 3

Tire circumference = 0.762 x 2 = 1.524 m = diameter

Circumference = π x D = 4.788 m

4.788 m/rev.
Speed of the stone = 4.788 x 122 = 584.186 m/min

Answer 4

[(2)(3,14)(.762)/122] (60)= speed of stone in meters per second

Around 2.35 m/s

Answer 5

First, convert revolutions/minute into radians/2d Tangential speed w = (2 hundred rev/min)(a million min/60 sec)[2(pi) radians/revolution) = 6.sixty seven pi radians/2d v = 3.33 pi m/s centripetal acceleration = v^2/r = r (w^2) a = (0.5000)(6.sixty seven)^2 a = 22.22 m/s^2