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20 RPM to Rad – Easy Conversion Explained

20 rpm is approximately 2.0944 radians per second.

To convert revolutions per minute (rpm) to radians per second (rad/sec), multiply by 2π (since one revolution equals 2π radians) and divide by 60 (seconds in a minute). So, 20 rpm equals (20 × 2π)/60, which simplifies to 2.0944 rad/sec.

Conversion Result

20 rpm equals roughly 2.0944 radians per second, meaning that an object rotating at 20 revolutions per minute completes about 2.0944 radians every second. This conversion helps in understanding rotational speeds in different measurement systems.

Conversion Tool


Result in rad:

Conversion Formula

The formula to convert rpm to rad/sec is: (rpm × 2π) / 60. This works because each revolution equals 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π gives radians per minute, then dividing by 60 converts it to radians per second. For example, 20 rpm: (20 × 2π)/60 = 2.0944 rad/sec.

Conversion Example

  • Convert 10 rpm to rad/sec:
    • Multiply 10 by 2π: 10 × 6.2832 = 62.832 radians per minute.
    • Divide by 60 seconds: 62.832 / 60 = 1.0472 rad/sec.
    • Result: 10 rpm is 1.0472 rad/sec.
  • Convert 50 rpm to rad/sec:
    • 50 × 2π = 314.159 radians per minute.
    • Divide by 60: 314.159 / 60 = 5.236 radians/sec.
    • Result: 50 rpm is 5.236 rad/sec.
  • Convert 5 rpm to rad/sec:
    • 5 × 2π = 31.416 radians per minute.
    • Divide by 60: 31.416 / 60 = 0.5236 rad/sec.
    • Result: 5 rpm equals 0.5236 rad/sec.
  • Convert 30 rpm to rad/sec:
    • 30 × 2π = 188.496 radians per minute.
    • Divide by 60: 188.496 / 60 = 3.1416 rad/sec.
    • Result: 30 rpm is 3.1416 rad/sec.

Conversion Chart

rpmrad/sec
-5.0 -0.5236
0.0 0.0000
5.0 0.5236
10.0 1.0472
15.0 1.5708
20.0 2.0944
25.0 2.6180
30.0 3.1416
35.0 3.6652
40.0 4.1888
45.0 4.7124

This chart shows rpm values from -5 to 45, alongside their rad/sec equivalents. To use it, find your rpm on the left and read across to see the corresponding rad/sec value. These conversions assist in quick reference for rotational speed measurements.

Related Conversion Questions

  • How many radians per second is 20 rpm?
  • What is the rad/sec equivalent of 20 rpm?
  • Convert 20 revolutions per minute to radians per second?
  • How do I change 20 rpm into rad/sec for motor speed calculations?
  • What is the angular velocity in radians/sec for 20 rpm?
  • Is 20 rpm equivalent to about 2 radians per second?
  • How do rpm and radians per second relate at 20 rpm?

Conversion Definitions

rpm

Revolutions per minute (rpm) measures how many full turns an object makes in a minute, used for rotational speed. It indicates how fast something spins, with higher rpm meaning faster rotation, and is common in motors, engines, and spinning machinery.

rad

Radians (rad) are units of angular measure representing the angle where the arc length equals the radius. One full circle equals 2π radians. Radians are used in mathematics and physics to describe rotation and angular displacement precisely.

Conversion FAQs

Why does multiplying rpm by 2π and dividing by 60 give rad/sec?

This works because multiplying rpm by 2π converts revolutions into radians, since each revolution is 2π radians. Dividing by 60 adjusts for seconds instead of minutes, converting the measure into radians per second, the standard SI unit for angular velocity.

Can I convert rpm to rad/sec without a calculator?

Yes, by memorizing common conversions or using approximate values. For example, 1 rpm equals approximately 0.1047 rad/sec, so multiply rpm by 0.1047 for a quick estimate. But for precise calculations, use the exact formula: (rpm × 2π)/60.

What are practical applications of converting rpm to rad/sec?

This conversion helps in designing and analyzing rotational systems like engines, turbines, and robotics. It allows engineers to work with angular velocities in SI units, which are essential for physics calculations, control systems, and mechanical specifications.

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Elara Bennett

Elara Bennett is the founder of PrepMyCareer.com website.

I am a full-time professional blogger, a digital marketer, and a trainer. I love anything related to the Web, and I try to learn new technologies every day.