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Converting 3600 rpm to radians per second results in approximately 376.99 rad/s.
To convert revolutions per minute (rpm) to radians per second (rad/s), multiply the rpm value by 2π and divide by 60. Since 1 revolution equals 2π radians, this formula converts the rotation speed into an angular velocity in radians per second.
Conversion Result
Result in rad:
Conversion Formula
The conversion from rpm to rad involves multiplying the rpm value by 2π, because one revolution is 2π radians, then dividing by 60 to convert minutes to seconds. The formula looks like: radians/sec = (rpm × 2π) / 60. This works because it directly relates rotation counts to angular displacement in radians.
For example, if you have 3600 rpm:
3600 × 2π = 22619.47 radians per minute. Then divide by 60: 22619.47 / 60 ≈ 376.99 rad/sec, which is the angular velocity in radians per second.
Conversion Example
- Convert 3000 rpm to rad/sec:
- Multiply 3000 by 2π: 3000 × 6.2832 = 18849.6 radians per minute.
- Divide by 60: 18849.6 / 60 ≈ 314.16 rad/sec.
- Convert 7200 rpm to rad/sec:
- 7200 × 2π = 45239.9 radians per minute.
- Divide by 60: 45239.9 / 60 ≈ 753.998 rad/sec.
- Convert 1500 rpm to rad/sec:
- 1500 × 2π = 9424.78 radians per minute.
- Divide by 60: 9424.78 / 60 ≈ 157.08 rad/sec.
- Convert 500 rpm to rad/sec:
- 500 × 2π = 3141.59 radians per minute.
- Divide by 60: 3141.59 / 60 ≈ 52.36 rad/sec.
- Convert 10000 rpm to rad/sec:
- 10000 × 2π = 62831.85 radians per minute.
- Divide by 60: 62831.85 / 60 ≈ 1047.2 rad/sec.
Conversion Chart
| rpm | rad/sec |
|---|---|
| 3575.0 | 374.74 |
| 3580.0 | 375.60 |
| 3585.0 | 376.45 |
| 3590.0 | 377.31 |
| 3595.0 | 378.16 |
| 3600.0 | 379.02 |
| 3605.0 | 379.87 |
| 3610.0 | 380.73 |
| 3615.0 | 381.58 |
| 3620.0 | 382.44 |
| 3625.0 | 383.29 |
This chart shows rpm values from 3575 to 3625 and their corresponding rad/sec conversions. To find a value, locate your rpm on the left column and read across to see the rad/sec equivalent.
Related Conversion Questions
- What is the rad/sec equivalent of 3600 rpm in a motor?
- How to convert 3600 rpm to radians per second for a rotating shaft?
- If a wheel spins at 3600 rpm, how many radians does it turn in one second?
- What is the angular velocity in radians/sec for 3600 rpm?
- How many radians per second correspond to 3600 rpm in a turbine?
- Can I quickly convert 3600 rpm to rad/sec without a calculator?
- What is the formula to convert rpm to radians per second for high-speed motors?
Conversion Definitions
rpm: Revolutions per minute measures how many complete turns an object makes in one minute, used in engineering and automotive contexts to describe rotational speeds.
rad: Radians are units of angular measure representing the ratio of an arc’s length to its radius, with 2π radians equaling one full revolution, used in mathematics and physics to quantify angles and rotations.
Conversion FAQs
How do I convert 3600 rpm to rad/sec manually?
To convert 3600 rpm to rad/sec, multiply 3600 by 2π and then divide by 60. This process accounts for converting revolutions to radians and minutes to seconds, giving approximately 376.99 rad/sec for 3600 rpm.
Why is it necessary to divide by 60 during conversion?
Dividing by 60 is necessary because rpm measures revolutions per minute, but radians per second require seconds as the time unit. This division adjusts the time base from minutes to seconds, aligning units correctly in the conversion process.
Can this conversion be used for any rpm value?
Yes, the formula (rpm × 2π) / 60 is universally applicable for converting any rpm value to radians per second, regardless of the magnitude, as it directly relates revolutions to radians and minutes to seconds.
