150 rpm is approximately 15.708 rad per second
Converting 150 rpm (revolutions per minute) to radians involves understanding that each revolution equals 2π radians, and there are 60 seconds in a minute. By multiplying 150 by 2π and then dividing by 60, we get the radian value per second.
Conversion Tool
Result in rad:
Conversion Formula
The conversion from rpm to radians involves multiplying the revolutions per minute (rpm) by 2π to get radians per minute, then dividing by 60 to convert to radians per second. This works because one revolution equals 2π radians, and there are 60 seconds in a minute.
For example, if you have 150 rpm, the math is:
- 150 rpm × 2π radians/revolution = 300π radians/minute
- 300π radians ÷ 60 seconds = 5π radians/sec
- Since π ≈ 3.1416, 5π ≈ 15.708 rad/sec
Conversion Example
Convert 200 rpm to rad/sec:
- Step 1: Multiply 200 by 2π: 200 × 6.2832 = 1256.64 radians/minute
- Step 2: Divide by 60: 1256.64 ÷ 60 ≈ 20.944 radians/sec
- This means 200 rpm equals approximately 20.944 rad/sec.
Convert 100 rpm to rad/sec:
- Step 1: 100 × 2π = 628.32 radians/minute
- Step 2: 628.32 ÷ 60 ≈ 10.472 radians/sec
- So, 100 rpm is roughly 10.472 rad/sec.
Convert 50 rpm to rad/sec:
- Step 1: 50 × 2π = 314.16 radians/minute
- Step 2: 314.16 ÷ 60 ≈ 5.236 radians/sec
- Hence, 50 rpm equals about 5.236 rad/sec.
Conversion Chart
| rpm | rad/sec |
|---|---|
| 125.0 | 13.089 |
| 130.0 | 13.613 |
| 135.0 | 14.137 |
| 140.0 | 14.661 |
| 145.0 | 15.185 |
| 150.0 | 15.708 |
| 155.0 | 16.232 |
| 160.0 | 16.756 |
| 165.0 | 17.280 |
| 170.0 | 17.804 |
| 175.0 | 18.328 |
This chart helps you find rad/sec values for rpm values between 125 and 175. Read across the row to see the corresponding rad/sec for each rpm value.
Related Conversion Questions
- How many radians per second is 150 rpm?
- What is the radian equivalent of 150 revolutions per minute?
- How do I convert 150 rpm to angular velocity in radians?
- What is the rad/sec value for a motor running at 150 rpm?
- Can you show me how to convert 150 rpm into radians per second?
- What is the formula to change rpm to radians?
- How many radians does a wheel turn per second at 150 rpm?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, indicating rotational speed. It is commonly used to describe engine, motor, or wheel rotation rates in various mechanical and engineering contexts.
rad
Radian (rad) is a unit of angular measurement representing the angle created when the arc length equals the radius. One radian equals approximately 57.2958 degrees, and it is used to express angles in mathematics and physics involving rotational motion.
Conversion FAQs
Why does multiplying rpm by 2π and dividing by 60 give radians per second?
This method works because each revolution covers 2π radians, and dividing by 60 converts minutes to seconds, resulting in the angular velocity in radians per second, which is standard in describing rotational speeds.
Can I convert rpm to radians per minute using the same formula?
Yes, but without dividing by 60, the result will be in radians per minute. To get radians per second, you must divide by 60 after multiplying by 2π.
What happens if I input a negative rpm value into the converter?
Negative rpm indicates rotation in the opposite direction. The converter will display a negative rad/sec value, reflecting the opposite rotational direction in the angular velocity.
Is there a difference between converting rpm to radians per second and degrees per second?
Yes, converting rpm to radians per second uses 2π, while degrees per second involves multiplying by 360 degrees per revolution and dividing by 60 seconds. The two units measure angular velocity but in different scales.