radians per second to millihertz conversion

How to convert radians per second to millihertz?

To convert radians per second (rad/s) to millihertz (mHz), you need to understand the relationship between these units of frequency.

1 radian per second can be converted to Hertz (Hz) first, and then to millihertz (mHz). Here’s the step-by-step process:

Conversion Steps:

1. Understand the Terms:

   • 1 Hertz (Hz) = 1 cycle per second.
   • 1 Radian per second (rad/s) is approximately equal to 0.159155 Hz.

2. Convert Radians per Second to Hertz:

   • 1 rad/s = 1 / (2π) Hz
   • ≈ 0.159155 Hz (since 2π ≈ 6.283185)

3. Convert Hertz to Millihertz:

   • 1 Hz = 1000 millihertz (mHz)
   • Therefore, 0.159155 Hz = 0.159155 * 1000 mHz
   • ≈ 159.155 mHz

So, 1 radian per second is approximately 159.155 millihertz (mHz).

Real-World Examples:

Here are some examples of different quantities of radians per second and their contexts:

1. 1 rad/s (159.155 mHz):

   • A common engineering calculation used in control systems and mechanical systems.

2. 2π rad/s (1 Hz or 1000 mHz):

   • Corresponds to one full cycle per second. It can be seen in electrical circuits operating at 1 Hz frequency (for instance, a very low-frequency oscillator).

3. 50 rad/s (~7.96 Hz or 7960 mHz):

   • This is within the range of rotational speeds in mechanical systems (like a small DC motor running at around 48 RPM).

4. 314 rad/s (~50 Hz or 50000 mHz):

   • The angular frequency of alternating current (AC) in power systems in most countries, where the AC frequency is 50 Hz.

5. 628 rad/s (100 Hz or 100000 mHz):

   • Angular frequency corresponding to typical audio signals. 100 Hz is within the audible range of human hearing (though on the lower end).

6. 27,000 rad/s (~4290.72 Hz or 4,290,720 mHz):

   • This is the angular frequency of ultrasound used in medical imaging where frequencies are in the range of 1 MHz (1 million Hz or 1 billion mHz).

These examples cover a broad range of applications, from mechanical and electrical engineering to acoustics and medical imaging, showing the versatility of the radians per second unit in measuring angular frequency and its conversions to different units.