How do you convert RPM to rad/s?
The Correct Answer and Explanation is :
To convert RPM (revolutions per minute) to rad/s (radians per second), you can use the following formula:
[
\text{rad/s} = \frac{\text{RPM} \times 2\pi}{60}
]
Explanation:
- Understanding the Units:
- RPM measures how many complete revolutions an object makes in one minute.
- A radian is a unit of angular measure used in mathematics and physics, where one full revolution corresponds to (2\pi) radians. Therefore, 1 revolution equals (2\pi) radians.
- Conversion Steps:
- Since RPM is expressed in revolutions per minute, to convert it to radians per second, we need to relate the two units. We start by recognizing that:
- 1 revolution = (2\pi) radians
- 1 minute = 60 seconds
- Thus, when we multiply RPM by (2\pi), we convert the revolutions to radians. However, since RPM is defined per minute, we must also account for the conversion from minutes to seconds by dividing by 60.
- Applying the Formula:
- For example, if you have an object rotating at 120 RPM:
[
\text{rad/s} = \frac{120 \times 2\pi}{60} = 4\pi \approx 12.57 \text{ rad/s}
] - This means that an object rotating at 120 RPM is making approximately 12.57 radians of rotation every second.
- Use Cases:
- This conversion is essential in various fields such as mechanical engineering, robotics, and physics, where understanding angular velocity is crucial for analyzing motion, designing systems, or modeling physical phenomena.
By using this conversion formula, you can easily switch between RPM and rad/s depending on the requirements of your calculations or applications.