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RPM (Revolutions Per Minute) and radians per second (rad/s) are both units used to measure rotational speed, but they differ in their scale and application. Below is an explanation of the relationship between RPM and rad/s.
RPM (Revolutions Per Minute):
RPM is a unit of rotational speed that indicates the number of complete revolutions per minute. It is commonly used in various applications, such as engines, motors, and centrifuges, to describe the speed of rotation.
Radians per Second (rad/s):
Radians per second is a unit of angular velocity, which measures the rate of change of angular displacement over time. It is an international standard unit in the metric system and is widely used in physics and engineering calculations.
To convert RPM to rad/s, you can use the following formula:
Angular Velocity (rad/s) = RPM × (2π / 60)
Here, 2π represents one complete revolution in radians (since one full circle is 360° or 2π radians), and dividing by 60 converts minutes to seconds.
Conversely, to convert rad/s to RPM, you can use the formula:
RPM = (Angular Velocity (rad/s) × 60) / 2π
Understanding the relationship between RPM and rad/s is crucial in various fields, such as mechanics, robotics, and automotive engineering, where precise control over rotational speed is essential.
By converting between these units, engineers and technicians can more accurately analyze and optimize the performance of rotating machinery.
The following table provides examples of RPM to rad/s conversions for various ranges:
| RPM | rad/s |
|---|---|
| 1 | 0.1047 |
| 2 | 0.2094 |
| 3 | 0.3142 |
| 4 | 0.4189 |
| 5 | 0.5236 |
| 6 | 0.6283 |
| 7 | 0.7330 |
| 8 | 0.8378 |
| 9 | 0.9425 |
| 10 | 1.0472 |
| 10 | 1.0472 |
| 20 | 2.0944 |
| 30 | 3.1416 |
| 40 | 4.1888 |
| 50 | 5.2360 |
| 60 | 6.2832 |
| 70 | 7.3304 |
| 80 | 8.3776 |
| 90 | 9.4248 |
| 100 | 10.4720 |
| 100 | 10.4720 |
| 200 | 20.9440 |
| 300 | 31.4159 |
| 400 | 41.8879 |
| 500 | 52.3599 |
| 600 | 62.8319 |
| 700 | 73.3038 |
| 800 | 83.7758 |
| 900 | 94.2478 |
| 1000 | 104.7198 |
| 1100 | 115.1917 |
| 1200 | 125.6637 |
| 1300 | 136.1357 |
| 1400 | 146.6077 |
| 1500 | 157.0796 |
| 1600 | 167.5516 |
| 1700 | 178.0236 |
| 1800 | 188.4956 |
| 1900 | 198.9675 |
| 2000 | 209.4395 |
| 2100 | 219.9115 |
| 2200 | 230.3835 |
| 2300 | 240.8554 |
| 2400 | 251.3274 |
| 2500 | 261.7994 |
| 2600 | 272.2714 |
| 2700 | 282.7433 |
| 2800 | 293.2153 |
| 2900 | 303.6873 |
| 3000 | 314.1593 |