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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:

$v_{(mph)} =\dfrac{3600.r}{1609.344} \times \omega_{(rad.s^{-1})}$

where:

- $v_{(mph)}$ is the linear velocity expressed in miles per hour [mph]
- $\omega_{(rad.s^{-1})}$ 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.

The formula to convert from radians per second to miles per hour is:

$\text{mph} = \text{rad/s} \times r \times \frac{3600}{1609.34}$

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).

If the radius $r$ is given in **miles**, the formula simplifies to:

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

If we have an angular velocity of $2 \, \text{rad/s}$ and a radius of $0.1$ miles, the linear velocity in mph is:

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

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