Hertz to radian/sec conversion

Hertz (Hz) and radians per second (rad/s) are both units of angular frequency. The conversion between these two units depends on the type of angular motion being considered.

For simple harmonic motion, where the angular velocity is directly proportional to the frequency, the conversion factor is 2π. Therefore:

Angular frequency in rad/s = Frequency in Hz × 2π

Conversely:

Frequency in Hz = Angular frequency in rad/s / (2π)

For example, let's say we have a frequency of 10 Hz and want to convert it to radians per second:

Angular frequency in rad/s = 10 Hz × 2π ≈ 62.83 rad/s

Similarly, if we have an angular frequency of 100 rad/s and want to convert it to Hertz:

Frequency in Hz = 100 rad/s / (2π) ≈ 15.92 Hz

Remember, this conversion factor specifically applies to simple harmonic motion. For other types of angular motion or more complex systems, the relationship between Hertz and radians per second may differ.