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

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

rad/s=mph×0.44704r\text{rad/s} = \frac { \text{mph} \times 0.44704 }{r}

or

ω=1609.3443600×vr\omega = \dfrac{1609.344}{3600} \times \frac{v}{r}

With the units:

ω(rad/s)=1609.3443600×v(mph)r(m)\omega_{(rad/s)}= \dfrac{1609.344}{3600} \times \frac{v_{ (mph) }}{r_{(m)}}

where:

  • v(mph)v_{(mph)} is the linear velocity expressed in miles per hour [mph]
  • ω(rad/s)\omega_{(rad/s)} is the angular velocity expressed in radians per second [rad/s]
  • r(m)r_{(m)} is the radius expressed in meters [m]

To convert miles per hour (mph) to radians per second (rad/s), you can use the following formula:

rad/s=mph×160×60×1609.34r\text{rad/s} = \text{mph} \times \frac{1}{60 \times 60} \times \frac{1609.34}{r}

Where:

  • mph\text{mph} is the speed in miles per hour.
  • 1609.341609.34 is the exact conversion factor from miles to meters (since 1 mile = 1609.34 meters).
  • 60×6060 \times 60 is the ratio between hours and seconds
  • rr is the radius in meters, which is necessary to convert linear velocity to angular velocity.

The steps are as follows:

  1. Convert mph to meters per second (m/s):

Convert mph to meters per second by multiplying by 1609.343600\frac{1609.34}{3600}.

vm.s1=1609.343600×v(mph)v_{m.s^{-1}} = \frac{1609.34}{3600} \times v_{ (mph) }

  1. Convert linear speed to angular speed:

Divide by the radius rr to convert to angular velocity in radians per second. Angular speed ω\omega in radians per second is given by ω=vr\omega = \frac{v}{r}, where vv is the linear speed in m/s and rr is the radius in meters.

ω(rad.s1)=vm.s1r=1609.343600×v(mph)r\omega_{(rad.s^{-1})} = \frac{v_{m.s^{-1}}}{r} = \frac{1609.34}{3600} \times \frac{v_{ (mph) }}{r}

Thus, the full formula is:

ω(rad/s)=1609.3443600×v(mph)r(m)\omega_{(rad/s)}= \dfrac{1609.344}{3600} \times \frac{v_{ (mph) }}{r_{(m)}}

So, combining these steps:

rad/s=mph×0.44704r\text{rad/s} = \frac{\text{mph} \times 0.44704}{r}

Disclaimer

This chatbot (Alphonsio) provides automated responses generated by machine-learning algorithms and relies on the accuracy of the underlying language models. While this Chatbot is programmed to provide accurate and relevant information, its information may not always be exhaustive, accurate, up-to-date or tailored to individual circumstances. It is not a substitute for professional advice or consultation with qualified experts. This chatbots and its responses are intended for informational purposes only and should not be used for commercial or business purposes. The creators of this chatbot are not liable for any damages or losses incurred as a result of using the information provided. By using our website, you acknowledge and agree to these terms. The data you submit to this chatbot is used to improve our algorithms. Under no circumstances should you submit sensitive data such as, but not limited to, personal data or passwords. The data you submit could then be made public.