degrees per second to hertz conversion

How to convert degrees per second to hertz?

To convert from degrees per second (°/s) to hertz (Hz), you need to understand the relationship between these units. Both units are measures of rotational speed, but in different ways.

1 degree of rotation is equivalent to 1/360th of a complete rotation because a full circle has 360 degrees.

Hertz (Hz) is a unit of frequency, and it represents the number of complete cycles per second. Therefore, to convert from degrees per second to hertz, you need to know how many complete rotations are happening per second.

Conversion calculation:

1 degree = 1/360 of a full rotation. Thus, 1 degree per second = (1/360) full rotations per second = (1/360) Hz.

So, 1 degree per second is equal to $\frac{1}{360} \approx 0.00278$ Hz.

Here are some real-world examples of quantities expressed in degrees per second:

1. Earth's Rotation:

   • The Earth rotates approximately 360 degrees in 24 hours.
   • Rotation speed is 360 degrees / (24 hours * 3600 seconds/hour) = 0.00417 degrees per second.

2. Fan Blades:

   • Suppose a ceiling fan rotates at 1200 RPM (revolutions per minute).
   • Convert RPM to degrees per second: $1200 \, \text{RPM} = 1200 / 60 \, \text{RPS} = 20 \, \text{RPS}$
   • Since 1 revolution is 360 degrees: $20 \, \text{RPS} \times 360 \, \text{degrees/revolution} = 7200 \, \text{degrees per second}$.
   • To convert to Hz: $7200 \, \text{degrees/second} \times (1 / 360) \approx 20 \, \text{Hz}$.

3. Record Player (Turntable):

   • A typical turntable might rotate at 33 1/3 RPM.
   • Convert RPM to degrees per second: $33.33 \, \text{RPM} = 33.33 / 60 \, \text{RPS} = 0.556 \, \text{RPS}$
   • Since 1 revolution is 360 degrees: $0.556 \, \text{RPS} \times 360 \, \text{degrees/revolution} \approx 200 \, \text{degrees per second}$.
   • To convert to Hz: $200 \, \text{degrees/second} \times (1 / 360) \approx 0.556 \, \text{Hz}$.

These examples should give you a sense of how degrees per second relates to practical, real-world situations and how to convert between degrees per second and hertz.