RPM To Angular Velocity: 5 Answers You Should Know


The rpm (revolutions per minute) and angular velocity both specify the rapidity of the rotating body. Let’s discuss how to change rpm to the angular velocity.

The conversion of rpm to angular velocity or vice versa can be done simply to determine the speed of the object. In physical or mechanical engineering, both these concepts determine how fast the particle or object is rotating about its fixed axis or on the circular path. 

Just like linear motion, there is rotational motion too. The quickness of the rotating body is determined by its angular velocity. For example, the wheel of a moving vehicle rotates on a fixed axis and on a circular path. Due to this motion, the angle keeps changing, and angular velocity emerges. 

Image Credit: dnet based on raster version released under GFDL, Angular velocityCC BY-SA 3.0

The angular speed or velocity of a rotating body defines how promptly the rotation is done on the circular path. Its unit is equal to radian per second. A complete circle measures 360°, so if a particle is completing 1 complete revolution in 1 second, then its angular velocity would be 360 degrees per second. In a radian per second unit, the angular velocity would equal 2π radians per second, as 360° is equal to 2π radians. 

RPM (revolutions per minute) also determines how fast the body rotates.1 complete rotation of the object makes up 1 revolution. The rate of the object becomes revolutions completed per minute.  

We can convert rpm to angular velocity in just simple steps. The standard unit of angular component of velocity is radian per second. Therefore for the conversion, the revolutions per minute have to be changed to radians per second. 

1 complete revolution completed by the rotating objects equals 360°. And 360° radians equals 2π radians. Therefore, 1 revolution equals to 2π radians that are;

1 revolution = 2π radians

Further, we know that 1 min = 60 seconds. 

Therefore the rpm to angular velocity become;

1revolution/1minute=2πradians/60seconds

[latex]\frac{1 revolution}{1 minute} = \frac{2\pi radians}{60 seconds}[/latex]

Thus we have;

1rpm=2π/60rad.s-1

[latex]1 rpm = \frac{2 \pi}{60} rad.s^{-1}[/latex]

The relationship between rpm and angular velocity becomes; 

ω=2π/60rpm

[latex]\omega = \frac{2 \pi}{60} rpm[/latex]

rpm to angular velocity

For example, a spinning wheel is rotating at the rate of 300 rpm. We can find the angular velocity as; 

The first step is to convert revolutions into radians. 

1 revolution = 2π

300 revolution = 300 x 2π = 600 π

The second step is to convert minutes into seconds.

1 minute = 60 seconds

Now the angular velocity would be

ω=radians/second

ω=600π/60

ω=10rad.s-1

[latex]\omega = \frac{radians}{second}[/latex]

[latex]\omega = \frac{600π}{60}[/latex]

[latex]\omega = 10 rad. s^{-1}[/latex]

Suppose a bicycle tire of 20 inches completes 420 revolutions in 1 minute. Then the angular velocity of the tire would be;

rpm=revolution/time

ω=2π/60*rpm

ω=2π/60*420

ω=4πrad.s-1

[latex]rpm = \frac{revolution}{time}[/latex]

[latex]\omega= \frac{2\pi}{60} \times rpm[/latex]

[latex]\omega = \frac{2\pi}{60} \times 420[/latex]

[latex]\omega = 4\pi rad.s^{-1}[/latex]

Frequently Asked Questions (FAQs)

Explain angular velocity with an example. 

The change in the angle of a rotating body constitutes its angular velocity. 

Suppose a spinning wheel is rotating. In doing so, it would move on a circular path. Now it moves from point A to point B, making angle theta in t seconds. Therefore the angular velocity of the wheel would be ω=θ/t [latex]\omega = \frac{\theta }{t}[/latex] . The unit of angular velocity is radian per second.

Is angular velocity a vector quantity?

The angular velocity is a vector quantity with both magnitude and direction. The direction of angular velocity acts along the axis of rotation of the body. 

What does rpm stand for? 

The rpm stands for revolution per minute. For a rotating body, the number of revolutions completed in one minute determines its rapidity. 

What is the angular velocity of the second hand of a clock? 

The second hand of a clock is a basic case of angular velocity.

The second hand of the clock finishes one complete revolution in one minute. We know that 1 revolution equals 2π radians and 1 minute equals 60 seconds. Therefore the angular velocity of the second hand is:

ω=2π/60

ω=π/30

ω=0.105rad.s-1

[latex]\omega = \frac{2 \pi}{60}[/latex]

[latex]\omega = \frac{\pi}{30}[/latex]

[latex]\omega = 0.105 rad. s^{-1}[/latex]

How to convert rpm to angular velocity? 

The rpm can be converted to the angular velocity in a few simple steps. 

Rpm is revolutions per minute. 1 revolution equals 360°, and 360° equals 2π radians. Therefore we have;

1 revolution = 2π radians

Secondly, 1 minute equals 60 seconds. 

Thus we have; 

1rpm=2π/60rad.s-1

ω=2π/60*rpm

[latex]1 rpm = \frac{2 \pi}{60} rad.s^{-1}[/latex]

[latex]\omega = \frac{2 \pi}{60} \times rpm[/latex]

Rabiya Khalid

Hi,  I am Rabiya Khalid, currently pursuing my masters in Mathematics. Article writing is my passion and I have been professionally writing for more than a year now. Being a science student, I have a knack for reading and writing about science and everything related to it. If you like what I write you can connect with me on LinkedIn: https://www.linkedin.com/mwlite/in/rabiya-khalid-bba02921a In my free time, I let out my creative side on a canvas. You can check my paintings at: https://www.instagram.com/chronicles_studio/

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