The result of converting 3600 rpm to radians per second is approximately 377 rad/sec.
To convert revolutions per minute (rpm) to radians per second (rad/sec), multiply the rpm value by 2π and then divide by 60. This is because one revolution equals 2π radians, and there are 60 seconds in a minute. So, the formula simplifies to rpm * (2π / 60).
Conversion Result
3600 rpm equals about 377 radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The conversion from rpm to rad involves multiplying the rpm value by 2π because each revolution is 2π radians. Since rpm is revolutions per minute, dividing by 60 converts minutes to seconds, resulting in radians per second. The formula is: radians/sec = rpm * (2π / 60).
For example, at 3600 rpm, multiply 3600 by 2π (approximately 6.2832), then divide by 60. That means 3600 * 6.2832 / 60 = 377 rad/sec. This calculation accounts for how many radians are covered in one second at that rpm rate.
Conversion Example
- Convert 1800 rpm:
- Multiply 1800 by 2π: 1800 * 6.2832 = 11309.76
- Divide by 60: 11309.76 / 60 = 188.5 rad/sec
- Convert 7200 rpm:
- Multiply 7200 by 2π: 7200 * 6.2832 = 45238.4
- Divide by 60: 45238.4 / 60 = 753.97 rad/sec
- Convert 1500 rpm:
- Multiply 1500 by 2π: 1500 * 6.2832 = 9424.8
- Divide by 60: 9424.8 / 60 = 157.08 rad/sec
- Convert 1200 rpm:
- Multiply 1200 by 2π: 1200 * 6.2832 = 7539.84
- Divide by 60: 7539.84 / 60 = 125.66 rad/sec
- Convert 2400 rpm:
- Multiply 2400 by 2π: 2400 * 6.2832 = 15078.4
- Divide by 60: 15078.4 / 60 = 251.31 rad/sec
Conversion Chart
| rpm | radians/sec |
|---|---|
| 3575.0 | 374.24 |
| 3580.0 | 374.94 |
| 3585.0 | 375.64 |
| 3590.0 | 376.34 |
| 3595.0 | 377.04 |
| 3600.0 | 377.75 |
| 3605.0 | 378.45 |
| 3610.0 | 379.15 |
| 3615.0 | 379.85 |
| 3620.0 | 380.55 |
| 3625.0 | 381.25 |
This chart displays rpm values from 3575 to 3625 and their corresponding rad/sec conversions. Use it to quickly find approximate conversions without calculations, especially in ranges close to 3600 rpm.
Related Conversion Questions
- What is the rad/sec equivalent of 3600 rpm in different units?
- How do I convert rpm to radians per second for high-speed motors?
- What is the formula to change rpm to rad/sec in motor calculations?
- Is there a quick way to estimate radians per second from rpm without calculator?
- How many radians per second is 3600 rpm in engineering applications?
- What are the steps to convert rpm to rad/sec manually?
- How does changing rpm affect the rad/sec value in mechanical systems?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, used to describe rotational speed in engines, motors, and machinery. It indicates the frequency of rotation but not the angular displacement directly.
rad
Rad, or radians, is a measure of angular displacement representing the angle subtended at the center of a circle by an arc equal in length to the circle’s radius. It provides a direct link between linear and angular measurements, used in physics and engineering.
Conversion FAQs
How do I convert 3600 rpm to radians per second manually?
To convert 3600 rpm to rad/sec, multiply by 2π to convert revolutions to radians, then divide by 60 to get per second. So, 3600 * 2π / 60 = 377 rad/sec. This process transforms rotational speed into an angular velocity measure.
Why is 2π used in the conversion formula from rpm to rad/sec?
Because one revolution equals 2π radians, the factor 2π converts revolutions into radians, which are a more fundamental angular measurement. Multiplying rpm by 2π ensures the conversion accounts for the total radians covered per revolution.
Can I convert rpm to rad/sec with a calculator or do I need a formula?
You can use a calculator by directly inputting the formula rpm * (2π / 60), which simplifies to rpm * 0.10472. Using the formula helps ensure accuracy and consistency across different calculations, especially for engineering purposes.
What is the significance of radians per second in physics?
Radians per second quantifies how fast an object rotates, describing the angular velocity in rotational motion. It is vital for analyzing dynamics, calculating torque, and understanding the behavior of rotating systems in physics and engineering.