The formula to convert radians per second [rad/s] to miles per hour [mph] is given by:
v(mph)=1609.3443600.r×ω(rad.s−1)
where:
- v(mph) is the linear velocity expressed in miles per hour [mph]
- ω(rad.s−1) is the angular velocity expressed in radians per second [rad/s]
- r is the radius expressed in meters [m]
To convert radians per second (rad/s) to miles per hour (mph), we need to know the radius of the circular path in which the object is moving. This is because radians per second represents angular velocity, while miles per hour represents linear velocity, which depends on the radius.
Formula
The formula to convert from radians per second to miles per hour is:
mph=rad/s×r×1609.343600
where:
- rad/s is the angular velocity in radians per second,
- r is the radius of the circular path in meters,
- 3600 is the number of seconds in an hour (for converting seconds to hours),
- 1609.34 is the number of meters in a mile (for converting meters to miles).
Simplified Formula (if Radius is Known in Miles)
If the radius r is given in miles, the formula simplifies to:
mph=rad/s×r×3600
Example Calculation
If we have an angular velocity of 2rad/s and a radius of 0.1 miles, the linear velocity in mph is:
mph=2×0.1×3600=720mph
This formula allows you to directly convert from radians per second to miles per hour based on the radius of the circular path.