millihertz to radians per second conversion

How to convert millihertz to radians per second?

Sure! To convert millihertz (mHz) to radians per second (rad/s), you need to follow these steps:

1. Understand the Units:

   • 1 millihertz (mHz) is $10^{-3}$ hertz (Hz).
   • Hertz is the unit of frequency indicating cycles per second.
   • One complete cycle is $2\pi$ radians.

2. Conversion Steps:

   • Convert millihertz to hertz: $1 \text{ mHz} = 0.001 \text{ Hz}$.
   • Convert Hz to radians per second: $1 \text{ Hz} = 2\pi \text{ rad/s}$.

So, to convert 1 mHz to rad/s:

$1 \text{ mHz} = 0.001 \text{ Hz} \times 2\pi \text{ rad/s/Hz} = 0.002\pi \text{ rad/s} \approx 0.00628 \text{ rad/s}$

Real-World Examples

Here are some examples of different millihertz frequencies and their contexts:

1. 0.3 mHz (0.0003 Hz):

   • This is approximately a period of around 55.6 minutes per cycle.
   • Example: Certain types of slow oscillations in geothermal activities can occur on this order.

2. 10 mHz (0.01 Hz):

   • This is equivalent to a period of 100 seconds per cycle.
   • Example: Slow-moving waves in large masses of water such as small seiches in enclosed basins or lakes.

3. 50 mHz (0.05 Hz):

   • Converts to a period of 20 seconds per cycle.
   • Example: Some low-frequency ocean wave oscillations could have such frequencies.

To find the quantity of radians per second for different millihertz frequencies:

$\text{Frequency in mHz} \times 0.002\pi \text{ (rad/s per mHz)}$

• 0.3 mHz: $0.3 \times 0.002\pi \text{ rad/s} \approx 0.001884 \text{ rad/s}$

• 10 mHz: $10 \times 0.002\pi \text{ rad/s} \approx 0.0628 \text{ rad/s}$

• 50 mHz: $50 \times 0.002\pi \text{ rad/s} \approx 0.314 \text{ rad/s}$

These examples and conversions provide a good understanding of how millihertz units correlate with more familiar time-based frequencies and angular velocities!