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The conversion of 200 rpm to radians per second results in approximately 20.943 rad/sec.
This is because 1 revolution per minute (rpm) equals 2π/60 radians per second. To convert 200 rpm, we multiply 200 by 2π/60, which simplifies to about 20.943 radians per second, giving us the angular velocity in radians.
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Conversion Result
Conversion Tool
Result in rad:
Conversion Formula
The formula used to convert rpm to radians per second is: radians/sec = rpm × (2π / 60).
This works because one revolution equals 2π radians, and there are 60 seconds in a minute. So, multiplying rpm by 2π/60 converts revolutions per minute into radians per second.
For example, at 200 rpm: 200 × (2π / 60) = 200 × 0.10472 ≈ 20.943 rad/sec.
Conversion Example
- Convert 150 rpm to radians/sec:
- Step 1: Write formula: radians/sec = 150 × (2π / 60)
- Step 2: Calculate 2π ≈ 6.2832
- Step 3: Divide 6.2832 by 60: ≈ 0.10472
- Step 4: Multiply 150 by 0.10472: ≈ 15.708 radians/sec
- Convert 300 rpm to radians/sec:
- Step 1: 300 × (2π / 60)
- Step 2: 2π ≈ 6.2832
- Step 3: 6.2832 / 60 ≈ 0.10472
- Step 4: 300 × 0.10472 ≈ 31.416 radians/sec
- Convert 100 rpm to radians/sec:
- Step 1: 100 × (2π / 60)
- Step 2: 2π ≈ 6.2832
- Step 3: 6.2832 / 60 ≈ 0.10472
- Step 4: 100 × 0.10472 ≈ 10.472 radians/sec
Conversion Chart
| rpm | rad/sec |
|---|---|
| 175.0 | 18.3016 |
| 180.0 | 18.8496 |
| 185.0 | 19.3976 |
| 190.0 | 19.9456 |
| 195.0 | 20.4936 |
| 200.0 | 20.9430 |
| 205.0 | 21.4900 |
| 210.0 | 22.0380 |
| 215.0 | 22.5860 |
| 220.0 | 23.1340 |
| 225.0 | 23.6820 |
This chart shows rpm values from 175 to 225 and their equivalent in radians per second. To find the radians/sec for a specific rpm, locate the rpm row and read its rad/sec value.
Related Conversion Questions
- How many radians per second is 200 rpm?
- What is the rad/sec equivalent of 200 rpm?
- How do I convert 200 rpm to radians in a calculator?
- What is 200 revolutions per minute in radians per second?
- Convert 200 rpm to radians: what is the speed in rad/sec?
- For 200 rpm, how many radians does the shaft rotate per second?
- How do I calculate radians/sec from rpm for 200 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 for engines, motors, and rotating machinery to quantify how fast they spin around an axis.
rad
Radians (rad) are units of angle measurement based on the radius of a circle. One radian equals the angle where the arc length equals the radius. Radians are widely used in mathematics and physics to express rotational quantities and angular displacement.
Conversion FAQs
Why is 1 rpm equal to (2π/60) radians per second?
This is because one revolution corresponds to 2π radians, and since there are 60 seconds in a minute, dividing 2π by 60 converts revolutions per minute to radians per second. It ensures angular velocity is measured correctly in rad/sec.
Can I convert rpm to radians per second manually?
Yes, by multiplying the rpm value by 2π/60, you directly convert revolutions per minute into radians per second. This simple formula accounts for the circle’s circumference and the time conversion from minutes to seconds.
What is the significance of radians in rotational calculations?
Radians facilitate precise calculations involving angles, arc lengths, and rotational velocities. They simplify formulas in physics and engineering by providing a natural measure for angular displacement, especially in calculus-based equations and trigonometry.
Is the conversion from rpm to rad/sec always linear?
Yes, because the relationship is governed by a constant factor (2π/60). Therefore, increasing rpm proportionally increases radians per second, making the conversion straightforward and linear.
