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The conversion of 10 rpm to radians per second results in approximately 1.0472 radians/sec.
Since 1 rpm means one revolution per minute, and one revolution equals 2π radians, to convert rpm to rad/sec, multiply rpm by 2π and divide by 60 seconds. For 10 rpm, multiply 10 by 2π (which is about 6.2832), then divide by 60, giving roughly 1.0472 rad/sec.
Conversion Formula
The formula to convert revolutions per minute (rpm) to radians per second (rad/sec) is:
rad/sec = (rpm × 2π) / 60
This works because each revolution has 2π radians, and there are 60 seconds in a minute. So, multiplying rpm by 2π converts revolutions to radians, and dividing by 60 converts minutes to seconds. For example, for 10 rpm: 10 × 2π = 62.832 radians per minute, then divide by 60 to get 1.0472 rad/sec.
Conversion Example
- Convert 20 rpm to rad/sec:
- Multiply 20 by 2π: 20 × 6.2832 = 125.664 radians per minute.
- Divide by 60 seconds: 125.664 / 60 = 2.0944 rad/sec.
- Convert 5 rpm to rad/sec:
- 5 × 6.2832 = 31.416 radians per minute.
- Divide by 60: 31.416 / 60 = 0.5236 rad/sec.
- Convert 15 rpm to rad/sec:
- 15 × 6.2832 = 94.248 radians per minute.
- Divide by 60: 94.248 / 60 = 1.5708 rad/sec.
Conversion Chart
| rpm | Radians/sec (rad/sec) |
|---|---|
| -15.0 | -1.5708 |
| -10.0 | -1.0472 |
| -5.0 | -0.5236 |
| 0.0 | 0 |
| 5.0 | 0.5236 |
| 10.0 | 1.0472 |
| 15.0 | 1.5708 |
| 20.0 | 2.0944 |
| 25.0 | 2.6179 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
This chart shows various rpm values and their equivalent in radians per second. To use it, find your rpm value in the first column and see the corresponding rad/sec in the second column.
Related Conversion Questions
- How many radians per second is 10 rpm?
- What is the rad/sec equivalent for 10 rpm?
- How do I convert 10 revolutions per minute to radians?
- What is 10 rpm in terms of radians per second?
- Can you show me the conversion of 10 rpm into radians?
- What is the formula for converting rpm to radians/sec for 10 rpm?
- How many radians does 10 rpm correspond to?
Conversion Definitions
rpm: Revolutions per minute measures how many complete turns something makes each minute, used to indicate rotational speeds in machinery and devices.
rad: Radian is a unit of angular measure, where one radian represents the angle at the center of a circle subtended by an arc equal in length to the radius.
Conversion FAQs
How accurate is the conversion from rpm to rad/sec?
The conversion is precise as it relies on fundamental mathematical constants and straightforward calculations, but slight variations might occur due to rounding in decimal approximations of pi or the calculation process.
Can I convert rad/sec back to rpm using the same formula?
Yes, reversing the process involves multiplying rad/sec by 60 and dividing by 2π, so the formula becomes rpm = (rad/sec × 60) / 2π.
Why is 2π used in the formula?
Because one revolution equals 2π radians, incorporating 2π in the formula converts revolutions into radians, which are more fundamental units of rotation measurement for angular velocities.
Is there a quick way to estimate rad/sec from rpm without calculation?
For rough estimates, multiply rpm by about 0.1047 (since 2π/60 ≈ 0.1047). For example, 10 rpm roughly equals 1.047 rad/sec, which is a handy approximation for quick calculations.