degrees per second to megahertz conversion

How to convert degrees per second to megahertz?

To convert degrees per second (°/s) to megahertz (MHz), you need to understand the relationship between degrees and cycles, and cycles and hertz (Hz).

1. Degrees and Cycles:

   • One complete cycle is 360 degrees.
   • Therefore, to convert degrees per second to cycles per second (Hz), you divide by 360.

2. Cycles per Second to Megahertz:

   • 1 cycle per second is 1 Hz.
   • 1 MHz is $10^6$ Hz.

Here’s the conversion step-by-step:

Step 1: Convert degrees per second to cycles per second (Hz). $\text{frequency in Hz} = \frac{\text{degrees per second}}{360}$

Step 2: Convert cycles per second (Hz) to megahertz (MHz). $\text{frequency in MHz} = \frac{\text{frequency in Hz}}{10^6}$

For 1 degree per second: $\text{frequency in Hz} = \frac{1 \, \text{degree per second}}{360} = \frac{1}{360} \, \text{Hz} \approx 0.00278 \, \text{Hz}$

Then, convert Hz to MHz: $\text{frequency in MHz} = \frac{0.00278 \, \text{Hz}}{10^6} = 2.78 \times 10^{-9} \, \text{MHz}$

So, 1 degree per second is approximately $2.78 \times 10^{-9} \, \text{MHz}$.

Real-World Examples for Other Quantities of Degrees per Second:

1. Turntable (Phonograph) Speed:

   • A standard turntable rotates at 33.33 RPM (revolutions per minute).
   • To convert RPM to degrees per second, note that 1 RPM = 6 degrees per second (since $1 \text{ revolution} = 360 \text{ degrees}$).
   • So, $33.33 \, \text{RPM} \approx 200 \, \text{degrees per second}$.
   • In MHz, $\frac{200}{360} \approx 0.5556 \, \text{Hz} = 0.5556 \times 10^{-6} \, \text{MHz} \approx 0.5556 \, \mu\text{Hz}$.

2. Clock’s Second Hand:

   • A clock's second hand completes one revolution per minute, which is 6 degrees per second.
   • In MHz, $\frac{6}{360} = 0.0167 \, \text{Hz} = 1.67 \times 10^{-8} \, \text{MHz}$.

3. Earth’s Rotation:

   • Earth completes a 360-degree rotation in 24 hours.
   • To find degrees per second: $\frac{360 \text{ degrees}}{86400 \text{ seconds}} \approx 0.00417 \text{ degrees/second}$.
   • In MHz, $\frac{0.00417}{360} \approx 1.16 \times 10^{-5} \, \text{Hz} = 1.16 \times 10^{-11} \, \text{MHz}$.

These conversions help place the original concept into a real-world context, showing the slow speed of rotation in terms that are understandable by relating to familiar objects.