degrees per second to kilohertz conversion

How to convert degrees per second to kilohertz?

To convert degrees per second (°/s) to kilohertz (kHz), you need to understand the relationship between degrees and cycles (or complete rotations), and how this relates to Hertz.

1. Understand the Basic Units:

   • One complete cycle (rotation) is 360 degrees.
   • Frequency in Hertz (Hz) measures cycles per second.
   • Kilohertz (kHz) is 1,000 Hertz.

2. Convert Degrees per Second to Cycles per Second (Hz):

   • Determine how many cycles per second you have for the given degrees per second.
   • For 1 degree per second: $\text{Cycles per second (Hz)} = \frac{\text{Degrees per second}}{360 \text{ degrees per cycle}} = \frac{1 \, \text{degree per second}}{360} \approx 0.00278 \, \text{Hz}$

3. Convert Hertz to Kilohertz:

   • Since 1 kHz = 1,000 Hz: $\text{Kilohertz (kHz)} = \frac{\text{Cycles per second (Hz)}}{1000} = \frac{0.00278 \, \text{Hz}}{1000} = 0.00000278 \, \text{kHz}$

Therefore, 1 degree per second is approximately 0.00000278 kilohertz (2.78 x 10^-6 kHz).

Real-World Examples for Other Quantities of Degrees per Second

1. Turntable at 33.3 RPM:

   • RPM (Revolutions Per Minute) to degrees per second: $33.3 \, \text{RPM} = 33.3 \times 360 \, \text{degrees per minute} = 11,988 \, \text{degrees per minute}$
   • Convert to degrees per second: $11,988 \, \text{degrees per minute} \div 60 = 199.8 \, \text{degrees per second}$
   • Convert to kHz: $\text{Cycles per second} = \frac{199.8}{360} \approx 0.555 \, \text{Hz}$ $\text{kHz} = \frac{0.555}{1000} = 0.000555 \, \text{kHz}$

2. Typical Motor Shaft Rotation at 1800 RPM:

   • RPM to degrees per second: $1800 \, \text{RPM} = 1800 \times 360 \, \text{degrees per minute} = 648,000 \, \text{degrees per minute}$
   • Convert to degrees per second: $648,000 \, \text{degrees per minute} \div 60 = 10,800 \, \text{degrees per second}$
   • Convert to kHz: $\text{Cycles per second} = \frac{10,800}{360} = 30 \, \text{Hz}$ $\text{kHz} = \frac{30}{1000} = 0.03 \, \text{kHz}$

3. Earth's Rotation:

   • Earth's rotation speed is approximately 15 degrees per hour (as it rotates 360 degrees in 24 hours).
   • Convert to degrees per second: $15 \, \text{degrees per hour} \div 3600 \, \text{seconds per hour} = 0.00417 \, \text{degrees per second}$
   • Convert to kHz: $\text{Cycles per second} = \frac{0.00417}{360} \approx 0.0000116 \, \text{Hz}$ $\text{kHz} = \frac{0.0000116}{1000} = 0.0000000116 \, \text{kHz}$

These conversions illustrate how degrees per second translate into Hertz and kilohertz. Remember, degrees per second measures rotational speed, whereas Hertz (and kilohertz) measures frequency, typically equated to cycles per second.