150 rpm equals approximately 15.7 radians per second
Converting 150 revolutions per minute (rpm) to radians involves multiplying by a factor that accounts for the full circle and time units. Since one revolution is 2π radians and there are 60 seconds in a minute, the conversion results in approximately 15.7 radians per second.
Introduction
When converting rpm to radians per second, the core idea is to change revolutions per minute into radians per second. The formula multiplies rpm by 2π (because each revolution is 2π radians) and divides by 60 (to convert minutes to seconds). This ensures the units align properly for angular velocity in rad/sec.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec multiplies the rpm value by 2π because there are 2π radians in each revolution. Then, it divides by 60 because there are 60 seconds in a minute, converting the time unit from minutes to seconds. For example, 150 rpm: 150 x 2π / 60 = 15.7 rad/sec.
Conversion Example
- Convert 200 rpm to rad/sec:
- Multiply 200 by 2π: 200 x 6.2832 ≈ 1256.64
- Divide by 60: 1256.64 / 60 ≈ 20.94 rad/sec
- Convert 90 rpm to rad/sec:
- Multiply 90 by 2π: 90 x 6.2832 ≈ 565.49
- Divide by 60: 565.49 / 60 ≈ 9.42 rad/sec
- Convert 300 rpm to rad/sec:
- Multiply 300 by 2π: 300 x 6.2832 ≈ 1884.96
- Divide by 60: 1884.96 / 60 ≈ 31.42 rad/sec
Conversion Chart
| rpm | Radians/sec |
|---|---|
| 125.0 | 13.09 |
| 130.0 | 13.59 |
| 135.0 | 14.09 |
| 140.0 | 14.66 |
| 145.0 | 15.16 |
| 150.0 | 15.71 |
| 155.0 | 16.21 |
| 160.0 | 16.76 |
| 165.0 | 17.26 |
| 170.0 | 17.76 |
| 175.0 | 18.31 |
This chart helps to quickly find the rad/sec equivalent for various rpm values. Read across the row to see the corresponding rad/sec for each rpm.
Related Conversion Questions
- How many radians per second is 150 rpm?
- What is the rad/sec value for 150 rpm in a motor?
- Convert 150 rpm to radians in a physics problem?
- If a wheel spins at 150 rpm, what is its angular velocity in radians?
- How do I convert revolutions per minute to radians per second for 150 rpm?
- What is the formula to change rpm to rad/sec for 150 rpm?
- At 150 rpm, how many radians does the wheel turn per second?
Conversion Definitions
rpm: Revolutions per minute measures how many complete turns an object makes in one minute, used in mechanical and rotational contexts to describe speed of rotation.
rad: Radians are a unit of angular measurement that describe the size of an angle based on the radius of a circle, with 2π radians equaling one full revolution.
Conversion FAQs
How can I quickly convert 150 rpm to radians per second?
Multiply 150 by 2π, then divide by 60 to get approximately 15.7 rad/sec. This method provides a fast way without a calculator, but using the formula is more precise for detailed calculations.
Why is 2π used in the conversion formula?
Because one revolution equals 2π radians, multiplying rpm by 2π converts revolutions into radians, aligning the angular measurement with the radian unit for proper angular velocity calculation.
What if I need to convert a different rpm value to radians?
Simply replace the 150 in the formula with your value: multiply by 2π, then divide by 60, to find the rad/sec equivalent for any rpm.
Is there a way to do this conversion without a calculator?
Yes, for common rpm values, you can memorize the result, or approximate 2π as 6.28 and perform mental math. For exact results, using a calculator or the conversion formula is recommended.
How does changing rpm affect radians per second?
Increasing rpm proportionally increases radians per second, as both units measure angular velocity. Lower rpm results in lower rad/sec, and vice versa, following the direct proportionality in the formula.