How do you convert radians per second into miles per hour?

Question

How do you convert radians per second into miles per hour? If you cannot explain...are there any sites that do? Thanks.

Answer 1

For example, in rotating anemometers conversions you would:


1. Measure the distance from the center of the rotating cup to the axis of rotation in inches and call it R.
2. Multiply R by 1/12 to get it into feet.
3. Find the number of revolutions the cup makes in a second (we would suggest you count the number of revolutions for 30 seconds and then divide the number of revolutions you get by 30--this will give you an average value). call that number w. It will have units of revolutions per second.
4. Multiply w by 2 pi (6.283053). This will convert the result to Radians per second since 2 pi radians = 1 revolution.
5. Multiply the result of step 2 with the result of step 4. The number you get will be the wind speed in feet per second
6. Multiply the number you get in step 5 by (3600/5280) to convert it to miles per hour.

Dr. H

Answer 2

Radians To Miles

Answer 3

If you have a spinning lever moving around an axle, you can find the speed of any point along a radius coming out from the central axis.

So look at what a radian IS first. The radian is the ratio of the circumference of a circle within the angle to the radius.

radius*radians/second = circumference distance in units of radians/second = 2*pi*radius(radians/radius)/second = 2*pi*radians/second

(2*pi*radians)/time = speed

The speed is in units of distance units used for the measure of the radus per second.

Do dimensional analysis to convert this to miles per hour.

Answer 4

There are 6.2832 radians in a full circle.

If a circle has a diameter of 2 miles, the circumference of the circle is 3.1416 x 2 miles = 6.2832 miles.

Therefore for this case each mile = one radian.

If a car is driving around the circle at one mile per hour, it's speed is also equal to one radian per hour therefore for this condition, 1 mile per hour = 1/3600 radian per second.

If the diameter of the circle is 4 miles the circumference of the circle is = 12.5664 miles. Therefore for this case each mile = 1/2 radian and for this condition a car driving on the circumference of the circle at 1 mile per hour = 1/7200 radians per second.

So the answer would be different for each circular arc.

Answer 5

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v = r*ω ω = v/r v = 50 mph = 50*5280*12/(3600) = 880 inches/sec ω = 880/16 = 55 radians/second

Answer 6

radians per second is an angular velocity, MPH is a linear velocity. So they are two different things.

If an object rolls without sliding however, its linear velocity = angular velocity*radius of object

Answer 7

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