hertz to radians per second conversion

How to convert hertz to radians per second?

Certainly! To convert hertz (Hz) to radians per second (rad/s), you need to understand the relationship between these units. Hertz is a measure of frequency, representing the number of cycles per second. Radians per second is a measure of angular velocity, representing the angle swept out per second.

The conversion between hertz and radians per second is based on the fact that one complete cycle (revolution) is equal to $2\pi$ radians. Therefore, 1 hertz (1 cycle per second) is equal to $2\pi$ radians per second.

Here's the conversion formula: $\text{Frequency (Hz)} \times 2\pi = \text{Angular Velocity (rad/s)}$

So, for 1 hertz: $1 \, \text{Hz} \times 2\pi \, \text{rad/Hz} = 2\pi \, \text{rad/s}$

Therefore, 1 Hz is equal to $2\pi \approx 6.2832$ radians per second.

Real-World Examples for Other Quantities of Hertz

50 Hz

• Electrical power systems in many parts of the world operate at 50 Hz. $50 \, \text{Hz} \times 2\pi \approx 314.16 \, \text{rad/s}$

60 Hz

• Electrical power systems in North America and some other regions operate at 60 Hz. $60 \, \text{Hz} \times 2\pi \approx 376.99 \, \text{rad/s}$

1 kHz (1000 Hz)

• This is a common frequency used in audio signals and communications. $1000 \, \text{Hz} \times 2\pi \approx 6283.19 \, \text{rad/s}$

440 Hz

• This is the standard pitch reference tone (A4) used for tuning musical instruments. $440 \, \text{Hz} \times 2\pi \approx 2764.60 \, \text{rad/s}$

2.45 GHz (2.45 x 10^9 Hz)

• This is the frequency used by microwave ovens and some Wi-Fi bands. $2.45 \times 10^9 \, \text{Hz} \times 2\pi \approx 1.54 \times 10^{10} \, \text{rad/s}$

These examples illustrate the conversion from hertz to radians per second and some common applications in different fields such as electrical engineering, audio, and telecommunications.