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400 rpm is approximately 41.89 radians
When converting 400 revolutions per minute (rpm) to radians, it equals roughly 41.89 radians. This conversion involves translating a rotational speed from revolutions per minute into radians per second, since radians measure angles, and seconds measure time. The calculation considers that one revolution is 2π radians and that there are 60 seconds in a minute.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: (rpm * 2π) / 60. This works because each revolution equals 2π radians, and there are 60 seconds in a minute. By multiplying rpm with 2π, you get radians per minute, then dividing by 60 converts it to radians per second. For example, 400 rpm: 400 * 2π / 60 = 41.89 rad/sec.
Conversion Example
- Convert 600 rpm:
- Step 1: Multiply rpm by 2π: 600 * 2π = 3769.91
- Step 2: Divide by 60: 3769.91 / 60 = 62.83 rad/sec
- Convert 250 rpm:
- Step 1: 250 * 2π = 1570.80
- Step 2: 1570.80 / 60 = 26.18 rad/sec
- Convert 900 rpm:
- Step 1: 900 * 2π = 5654.87
- Step 2: 5654.87 / 60 = 94.25 rad/sec
- Convert 100 rpm:
- Step 1: 100 * 2π = 628.32
- Step 2: 628.32 / 60 = 10.47 rad/sec
Conversion Chart
| rpm | Radians/sec |
|---|---|
| 375.0 | 39.27 |
| 380.0 | 39.80 |
| 385.0 | 40.33 |
| 390.0 | 40.86 |
| 395.0 | 41.39 |
| 400.0 | 41.89 |
| 405.0 | 42.42 |
| 410.0 | 42.95 |
| 415.0 | 43.48 |
| 420.0 | 44.01 |
| 425.0 | 44.55 |
This chart helps quickly find the rad/sec value for rpm values ranging from 375 to 425. To read it, locate your rpm value in the first column, then look across to find the corresponding radians/sec in the second column.
Related Conversion Questions
- What is the radian equivalent of 400 rpm in a mechanical system?
- How many radians does a motor rotating at 400 rpm cover in one second?
- Can I convert 400 rpm into radians per hour, and how?
- What is the angular velocity in radians/sec for 400 rpm?
- How do I calculate radians from revolutions per minute for a rotating shaft?
- What is the formula to change 400 rpm into radians per second?
- Is there an easy way to convert rpm to radians for high-speed turbines?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, indicating rotational speed. It is used in machinery, engines, and motors to specify how fast parts are spinning, with higher rpm meaning faster rotation.
rad
Radians (rad) measure angles based on the radius of a circle, where 2π radians equal one full revolution. It is a standard angular unit in mathematics and physics, used to describe rotations, angles, and angular velocities precisely.
Conversion FAQs
How does changing rpm affect the radians per second?
Increasing rpm linearly increases radians per second because the conversion formula directly multiplies rpm by 2π/60. This means a higher rpm results in a proportionally higher angular velocity in radians/sec.
Why is 2π used in the conversion from rpm to radians?
2π radians equals one full revolution, so multiplying rpm by 2π converts revolutions into radians, enabling angular measurements in the standard radian unit rather than revolutions, which are more abstract mathematically.
Can I convert rpm to radians per minute instead of seconds?
Yes, but you need to omit dividing by 60. The formula becomes rpm * 2π, which gives the angular velocity in radians per minute. To get radians per second, you divide the result by 60.
