30 rpm is approximately 3.14 radians per second.
Converting 30 rpm to radians involves multiplying the revolutions per minute by a factor to get radians per second. Since there are 2π radians in a revolution and 60 seconds in a minute, the conversion uses these constants to change rpm to rad/sec.
Understanding the conversion from rpm to rad
To convert rpm to rad/sec, you need to know that one revolution is 2π radians, and one minute has 60 seconds. So, multiply the rpm value by 2π to get radians per minute, then divide by 60 to convert to radians per second. This process ensures the units are correctly aligned.
Conversion Tool
Result in rad:
Conversion Formula
The conversion formula from rpm to rad/sec is: radians per second = rpm * 2π / 60. This works because each revolution equals 2π radians, and dividing by 60 converts minutes to seconds. For example, 30 rpm: 30 * 2π / 60 = (30 * 6.2832) / 60 = 188.496 / 60 = 3.14 rad/sec.
Conversion Example
- Convert 10 rpm:
- Multiply 10 by 2π: 10 * 6.2832 = 62.832
- Divide 62.832 by 60: 62.832 / 60 = 1.0488 rad/sec
- Convert 50 rpm:
- 50 * 6.2832 = 314.16
- 314.16 / 60 = 5.236 rad/sec
- Convert 75 rpm:
- 75 * 6.2832 = 471.24
- 471.24 / 60 = 7.854 rad/sec
- Convert 5 rpm:
- 5 * 6.2832 = 31.416
- 31.416 / 60 = 0.5236 rad/sec
- Convert 55 rpm:
- 55 * 6.2832 = 345.83
- 345.83 / 60 = 5.763 rad/sec
Conversion Chart
| rpm | rad/sec |
|---|---|
| 5.0 | 0.524 |
| 10.0 | 1.047 |
| 15.0 | 1.571 |
| 20.0 | 2.094 |
| 25.0 | 2.618 |
| 30.0 | 3.142 |
| 35.0 | 3.665 |
| 40.0 | 4.189 |
| 45.0 | 4.712 |
| 50.0 | 5.236 |
| 55.0 | 5.759 |
This chart shows the rpm values in the first column and their equivalent in radians per second in the second. Use it to quickly find conversions for common rpm values.
Related Conversion Questions
- How many radians per second is 30 rpm?
- What is the rad/sec equivalent of 30 revolutions per minute?
- Convert 30 rpm to radians per second step-by-step?
- Is 30 rpm equal to 3.14 rad/sec?
- How do I convert rpm to radians in a formula?
- What is the meaning of rpm in radians per second?
- How do I calculate rad/sec from rpm for motor speed?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute. It counts rotations, not the angle, and is often used to describe motor speed or rotational velocity in mechanical systems.
rad
Rad (radian) is a unit of angular measurement that represents the angle where the arc length equals the radius. One radian equals approximately 57.2958 degrees, and it’s used to express angles in circular and rotational calculations.
Conversion FAQs
What is the formula to convert rpm to rad/sec?
The formula is radians per second equals rpm multiplied by 2π, then divided by 60. This accounts for the number of radians in a revolution and converts minutes to seconds, giving you the angular velocity in rad/sec.
Why is 2π used in the conversion?
Because one revolution is 2π radians, using 2π ensures the conversion from rotations to radians is accurate. Multiplying rpm by 2π converts revolutions to radians, aligning units for angular velocity calculations.
Can I convert rpm to rad/sec without a calculator?
Yes, by using approximate values like 6.2832 for 2π, or by memorizing key conversions, you can estimate rad/sec. For example, 30 rpm is roughly 3.14 rad/sec, which is close enough for many practical purposes.
How does the conversion change if the rotation speed doubles?
If the rpm doubles, then the rad/sec value also doubles because the conversion is directly proportional. For example, 30 rpm converts to 3.14 rad/sec, so 60 rpm would be approximately 6.28 rad/sec.