The conversion of 20 rpm to radians per second results in approximately 2.0944 rad/sec.
To convert revolutions per minute (rpm) to radians per second, we multiply the rpm value by 2π (since one revolution equals 2π radians) and divide by 60 (seconds in a minute). This process transforms the rotational speed from revolutions per minute to radians per second, a standard SI unit for angular velocity.
Conversion Result
20 rpm = 2.0944 rad/sec
Conversion Tool
Result in rad:
Conversion Formula
The conversion from rpm to rad/sec uses the formula: radians per second = (rpm × 2π) / 60. This works because each revolution is 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π converts revolutions to radians, then dividing by 60 adjusts for seconds.
For example, with 20 rpm: (20 × 2π) / 60 = (20 × 6.2832) / 60 = 125.664 / 60 ≈ 2.0944 rad/sec. This step-by-step process ensures precise conversion from revolutions per minute to angular velocity in radians per second.
Conversion Example
- Convert 10 rpm:
- Multiply 10 by 2π: 10 × 6.2832 = 62.832
- Divide by 60: 62.832 / 60 = 1.0472 rad/sec
- Convert 50 rpm:
- 50 × 6.2832 = 314.16
- 314.16 / 60 = 5.236 rad/sec
- Convert 5 rpm:
- 5 × 6.2832 = 31.416
- 31.416 / 60 = 0.5236 rad/sec
- Convert 100 rpm:
- 100 × 6.2832 = 628.32
- 628.32 / 60 = 10.472 rad/sec
Conversion Chart
| rpm | Radians/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 |
Use this chart to quickly find the rad/sec equivalent for a range of rpm values. Read across the row to see the corresponding rad/sec for each rpm value listed.
Related Conversion Questions
- What is 20 rpm in radians per second and how does the conversion work?
- How do I convert 20 rpm to radians per second manually?
- What is the angular velocity in radians/sec for 20 rpm?
- Can I convert 20 rpm to radians per second using a calculator?
- What is the formula to change rpm into radians per second for 20 rpm?
- How many radians per second is 20 rpm equivalent to in SI units?
- What are the steps to convert 20 rpm into rad/sec?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns a rotating object makes each minute. It is used in machinery and engines to describe rotational speeds, with higher rpm indicating faster spinning, and is converted into radians per second for scientific calculations.
rad
Rad, short for radians, is a unit measuring angles based on the radius of a circle. One radian equals the angle where the arc length equals the radius. It provides a natural measure for angular displacements, especially in physics and engineering, relating to rotation and oscillation.
Conversion FAQs
How does changing rpm affect radians per second?
Increasing rpm directly increases radians per second because both measure rotational speed, with radians per second providing a more universal and SI-compatible measure of angular velocity. The conversion formula ensures this change is precise.
Why is 2π used in the conversion formula?
2π represents one full revolution in radians, because a circle’s circumference corresponds to 2π radians. Multiplying rpm by 2π converts revolutions into radians, making it possible to express rotational speed in a continuous, angular measure.
What are common applications for rad/sec measurements?
Rad/sec are used in physics and engineering to analyze rotational dynamics, such as in motor speeds, angular acceleration, and oscillatory systems. They allow for mathematical modeling of rotational motion in a standardized unit compatible with calculus.