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Angular Velocity given Speed in RPM Calculator

Formula

The formula to calculate Angular Velocity (ω) is:

$ω = \frac{2 \cdot \pi \cdot N_A}{60}$

Where:

$ω$ is the Angular Velocity.
$N_A$ is the Speed of Shaft A in RPM.
$\pi$ is Archimedes' constant, approximately 3.141592653589793.

Definition

Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e., how fast the angular position or orientation of an object changes with time.

Speed of Shaft A in RPM is the speed at which the shaft tends to vibrate violently in the transverse direction.

How to calculate Angular Velocity given Speed in RPM

Let's assume the following values:

Speed of Shaft A in RPM (N_A) = 9

Using the formula:

$ω = \frac{2 \cdot \pi \cdot N_A}{60}$

Evaluating:

$ω = \frac{2 \cdot \pi \cdot 9}{60}$

The Angular Velocity is 0.942477796076938 rad/s.

Angular Velocity Conversion Chart

Speed of Shaft A in RPM (N_A)	Angular Velocity (ω)
5	0.523598775598299
6	0.628318530717959
7	0.733038285837618
8	0.837758040957278
9	0.942477796076938
10	1.047197551196598
11	1.151917306316257
12	1.256637061435917
13	1.361356816555577
14	1.466076571675237
15	1.570796326794896