1800 rpm is approximately 188.50 radians per second.
To convert revolutions per minute (rpm) to radians per second (rad/sec), multiply the rpm value by 2π and divide by 60. Since 1 revolution equals 2π radians, this conversion accounts for the full circle in radians, and dividing by 60 adjusts from minutes to seconds.
Conversion Result
Result in rad:
Conversion Formula
The conversion from rpm to rad involves multiplying the rpm value by 2π, because each revolution contains 2π radians. Then, dividing by 60 converts minutes into seconds, since there are 60 seconds in a minute. So, the formula is: (rpm) * 2π / 60 = rad/sec.
For example, for 1800 rpm: 1800 * 2π / 60 = (1800 / 60) * 2π = 30 * 2π = 30 * 6.2832 = 188.50 rad/sec.
Conversion Example
- Convert 900 rpm:
- Divide 900 by 60: 900 / 60 = 15
- Multiply 15 by 2π: 15 * 6.2832 = 94.248 rad/sec
- Convert 3600 rpm:
- Divide 3600 by 60: 3600 / 60 = 60
- Multiply 60 by 2π: 60 * 6.2832 = 376.99 rad/sec
- Convert 1500 rpm:
- Divide 1500 by 60: 1500 / 60 = 25
- Multiply 25 by 2π: 25 * 6.2832 = 157.08 rad/sec
Conversion Chart
| RPM | Radians per second |
|---|---|
| 1775.0 | 185.58 |
| 1780.0 | 186.17 |
| 1785.0 | 186.75 |
| 1790.0 | 187.34 |
| 1795.0 | 187.92 |
| 1800.0 | 188.50 |
| 1805.0 | 189.09 |
| 1810.0 | 189.67 |
| 1815.0 | 190.26 |
| 1820.0 | 190.84 |
| 1825.0 | 191.43 |
This chart shows rpm values from 1775 to 1825 and their equivalent in radians per second, useful for quick reference during conversions.
Related Conversion Questions
- How many radians per second are there in 1800 rpm?
- What is the rad/sec equivalent of 1800 revolutions per minute?
- Convert 1800 rpm to radians per second step-by-step?
- Why does multiplying rpm by 2π and dividing by 60 give radians per second?
- What is the formula to convert rpm to rad/sec for 1800 rpm?
- How do I convert 1800 rpm to angular velocity in radians per second?
- What is the rad/sec value for 1800 rpm?
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 engines, motors, and various mechanical systems to quantify how fast something spins around an axis.
rad
Rad, short for radians, is a unit of angular measurement representing the angle formed when an arc length equals the radius of a circle. It provides a natural way to measure angles based on the circle’s geometry, with 2π radians equaling one full revolution.
Conversion FAQs
What is the significance of converting rpm to radians per second?
Converting rpm to radians per second allows for precise calculations of angular velocity in physics and engineering, especially in dynamics, control systems, and rotational motion analysis. It provides a standard SI unit for angular speed.
Can I convert rpm to rad/sec manually or do I need a calculator?
Manual conversion is straightforward using the formula (rpm * 2π) / 60, but a calculator helps avoid errors, especially with larger numbers or when precise results are needed. Just input the rpm value, and the calculator computes rad/sec.
Does the conversion change for different rotational directions?
No, the conversion from rpm to radians per second measures magnitude of angular velocity regardless of direction. To account for direction, a sign (positive or negative) is added depending on rotation sense, but the conversion formula remains the same.