Which one of the following is the correct relation between frequency/and angular frequency a ?

The correct answer is Option 2: ω = 2πf.

In physics, particularly in wave mechanics and simple harmonic motion, the relationship between linear frequency and angular frequency is fundamental:

• Frequency (f): Represents the number of cycles or revolutions completed per unit time, measured in Hertz (Hz) or s⁻¹.
• Angular Frequency (ω): Represents the rate of change of the angular displacement, measured in radians per second (rad/s).

Since one complete cycle corresponds to a rotation of 2π radians, the angular frequency is calculated by multiplying the linear frequency by 2π. Thus, the formula is ω = 2πf.

Other options are incorrect because they fail to maintain this mathematical identity. For instance, Option 3 (f = ω/2π) is a correct derivation, but the question specifically asks for the relation in the form provided in Option 2. Options 1 and 4 represent incorrect mathematical ratios between these two physical quantities.