Samantha Nicole20 rpm is approximately 2.0944 radians per second
Converting 20 rpm to radians involves multiplying the revolutions per minute by a factor to convert rotations into radians, resulting in about 2.0944 rad/sec. This tells us how many radians are swept out each second at that rotational speed.
Introduction
When we convert from rpm (revolutions per minute) to radians, we are translating a rotational speed into an angular measure. Since one revolution equals 2π radians, the process involves converting minutes to seconds and revolutions to radians, giving us a precise angular velocity in rad/sec.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to radians per second is: radians/sec = (rpm) * (2π) / 60. This works because one revolution contains 2π radians, and minutes are converted to seconds by dividing by 60. The multiplication adjusts revolutions into radians per second.
For example, converting 20 rpm: 20 * (2π) / 60 = (20 * 6.2832) / 60 = 125.664 / 60 = 2.0944 rad/sec. This step-by-step calculation shows how each component contributes to the final angular velocity in rad/sec.
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 100 rpm:
- 100 * 6.2832 = 628.32
- 628.32 / 60 = 10.472 rad/sec
- Convert 5 rpm:
- 5 * 6.2832 = 31.416
- 31.416 / 60 = 0.5236 rad/sec
Conversion Chart
| rpm | rad/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 in the first column and their rad/sec equivalents in the second. To use it, find your rpm in the first column then read across to see the corresponding radians per second.
Related Conversion Questions
- How many radians per second is 20 rpm?
- What is the rad/sec equivalent of 20 rpm?
- Convert 20 rpm to angular velocity in radians per second?
- How do I change 20 rpm into radians per second?
- What is the rad/sec value for a motor spinning at 20 rpm?
- If a wheel rotates at 20 rpm, how many radians does it cover per second?
- At 20 rpm, what is the angular displacement in radians per second?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute. It is a rotational speed used in engines, motors, and machinery, indicating how fast something spins around an axis.
rad
Radian (rad) is a unit of angular measurement representing the angle created when the arc length equals the radius. It allows us to quantify rotations and angles in more precise mathematical calculations related to circles.
Conversion FAQs
Can I convert rpm directly to radians without any formula?
No, because rpm measures revolutions per minute while radians measure angles. You need to multiply by 2π to convert revolutions into radians and adjust for time units, typically seconds, to get radians per second.
Why do we divide by 60 in the conversion?
Dividing by 60 converts minutes into seconds, because there are 60 seconds in a minute. This step ensures the angular velocity is expressed in radians per second, standard for many physics and engineering applications.
What is the significance of 2π in the conversion?
2π radians is the measure of one complete revolution around a circle. Multiplying revolutions per minute by 2π converts the rotation count into radians, which are a more fundamental measure of angles in mathematics and physics.
Can I use this conversion for rotational speeds in different units?
Yes, but you must adjust the formula accordingly. For example, if your rotational speed is in revolutions per hour, you would multiply by 2π and divide by 3600 seconds per hour to get radians per second.
