1 Hertz (Hz) in the radians system is equivalent to what?

To understand why 1 Hertz (Hz) is equivalent to 2π radians/second, we need to first define what Hertz represents. One Hertz is defined as one cycle or oscillation per second. When dealing with rotational motion or waves, such as in physics and engineering, we often express angles in terms of radians rather than degrees.

In a complete cycle of rotation, an object travels through an angle of 2π radians. Therefore, if an object completes one full revolution (which is one cycle) each second, it has traveled through an angle of 2π radians in that one second.

Thus, when we say something has a frequency of 1 Hz, it means it completes one cycle per second, which corresponds to an angular velocity of 2π radians per second. This relationship is crucial in converting between frequency in hertz and angular displacement in radians.

Given this reasoning, the correct equivalence of 1 Hz in the context of radians is 2π radians/second, as it captures the total angular displacement associated with completing one full cycle in one second.