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What is the formula to convert radians per second [rad/s] to miles per hour [mph]?
alphonsio

The formula to convert radians per second [rad/s] to miles per hour [mph] is given by:

v(mph)=3600.r1609.344×ω(rad.s1)v_{(mph)} =\dfrac{3600.r}{1609.344} \times \omega_{(rad.s^{-1})}

where:

  • v(mph)v_{(mph)} is the linear velocity expressed in miles per hour [mph]
  • ω(rad.s1)\omega_{(rad.s^{-1})} is the angular velocity expressed in radians per second [rad/s]
  • rr 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×36001609.34\text{mph} = \text{rad/s} \times r \times \frac{3600}{1609.34}

where:

  • rad/s is the angular velocity in radians per second,
  • rr is the radius of the circular path in meters,
  • 36003600 is the number of seconds in an hour (for converting seconds to hours),
  • 1609.341609.34 is the number of meters in a mile (for converting meters to miles).

Simplified Formula (if Radius is Known in Miles)

If the radius rr is given in miles, the formula simplifies to:

mph=rad/s×r×3600\text{mph} = \text{rad/s} \times r \times 3600

Example Calculation

If we have an angular velocity of 2rad/s2 \, \text{rad/s} and a radius of 0.10.1 miles, the linear velocity in mph is:

mph=2×0.1×3600=720mph\text{mph} = 2 \times 0.1 \times 3600 = 720 \, \text{mph}

This formula allows you to directly convert from radians per second to miles per hour based on the radius of the circular path.