To convert angular velocity from radians per second (rad/s) to revolutions per minute (rpm), you can use the following formula:

$$N= \dfrac{60}{ 2 \pi } \times \omega$$

$$N_{(rpm)}= \dfrac{60}{ 2 \pi } \times \omega_{(rad/s)}$$

with :

• $\omega_{(rad/s)}$ the angular velocity expressed in radians per second [rad/s]
• $N_{(rpm)}$ the angular velocity expressed in revolution per minute [rpm]

Explanation:

• 1 revolution is equivalent to $2\pi$ radians.
• 1 minute is equivalent to 60 seconds.

So, to convert rad/s to rpm:

1. Multiply the angular velocity by 60 to account for the conversion from seconds to minutes.
2. Divide by $2\pi$ to convert radians to revolutions.

Simplified formula:

$$\text{rpm} = \text{rad/s} \times \frac{60}{6.2832} \approx \text{rad/s} \times 9.5493$$

We can deduce the following simplified formulas:

• 1 rad/s ≈ 9.5492965855 rpm
• 1 rpm = 0.10471975511965977 rad/s

Thus, multiplying the value in rad/s by approximately 9.5493 will give you the value in rpm.