1200 rpm equals approximately 125.66 radians per second.
Converting 1200 rpm to radians involves multiplying the revolutions per minute by a conversion factor to get radians per second. Since there are 2π radians in one revolution and 60 seconds in a minute, the calculation simplifies to multiplying rpm by 2π/60.
Introduction
The conversion from revolutions per minute (rpm) to radians per second (rad/sec) is a common task in physics and engineering. It helps understand how fast an object rotates in terms of angular distance covered over time. This conversion uses a simple mathematical formula based on the relationship between revolutions and radians.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: radians per second = rpm * (2π / 60). This formula works because one revolution equals 2π radians, and there are 60 seconds in a minute. By multiplying rpm by 2π/60, we convert revolutions to radians and minutes to seconds.
For example, converting 60 rpm:
- Multiply 60 by 2π: 60 * 6.2832 = 376.99
- Divide by 60: 376.99 / 60 = 6.2832 rad/sec
Conversion Example
- Convert 1500 rpm:
- Step 1: 1500 * 2π = 1500 * 6.2832 = 9424.8
- Step 2: 9424.8 / 60 = 157.08 rad/sec
- Convert 300 rpm:
- Step 1: 300 * 2π = 300 * 6.2832 = 1884.96
- Step 2: 1884.96 / 60 = 31.41 rad/sec
- Convert 900 rpm:
- Step 1: 900 * 2π = 900 * 6.2832 = 5654.88
- Step 2: 5654.88 / 60 = 94.25 rad/sec
Conversion Chart
| rpm | Radians/sec |
|---|---|
| 1175.0 | 123.12 |
| 1180.0 | 123.48 |
| 1185.0 | 123.84 |
| 1190.0 | 124.20 |
| 1195.0 | 124.56 |
| 1200.0 | 124.92 |
| 1205.0 | 125.28 |
| 1210.0 | 125.64 |
| 1215.0 | 126.00 |
| 1220.0 | 126.36 |
| 1225.0 | 126.72 |
This chart provides quick reference for converting rpm values in the range from 1175 to 1225 to radians per second. You can find your rpm value in the first column and read the corresponding rad/sec value in the second.
Related Conversion Questions
- How many radians per second is 1200 rpm?
- What is the rad/sec value for 1200 rpm?
- How do I convert 1200 rpm to angular velocity in radians?
- What is the radian measure equivalent to 1200 rpm?
- Can I convert 1200 rpm directly into radians per second?
- What formula should I use to convert rpm to radians per second for 1200 rpm?
- How fast in radians per second is a 1200 rpm motor rotating?
Conversion Definitions
rpm
Revolutions per minute (rpm) is a measurement of rotational speed, indicating how many complete turns an object makes in one minute. It is used to describe the speed of engines, turbines, and other rotating equipment.
rad
Radian (rad) is a unit of angular measurement representing the angle subtended at the center of a circle by an arc equal in length to the radius. It provides a direct measure of rotation in terms of the circle’s geometry.
Conversion FAQs
Why is the conversion factor 2π/60 used for rpm to rad/sec?
This factor is derived from the fact that one revolution equals 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π/60 converts revolutions per minute into radians per second, aligning the units correctly for angular velocity.
Can I convert rpm to rad/sec without using a calculator?
Yes, by remembering the approximate value of 2π as 6.2832, you can multiply your rpm by this number and then divide by 60, either mentally or with simple calculations, to get radians per second.
What is the significance of radians per second in rotational motion?
Radians per second measure how quickly an object rotates around its axis, directly relating to angular velocity. It is essential for calculating kinetic energy, acceleration, and other dynamic properties in rotational systems.