Physics · Waves · NEET
No. Frequency f counts how many full cycles happen each second (unit hertz). Angular frequency omega measures how many radians the particle sweeps each second (unit rad/s). One cycle is 2 pi radians, so they are linked by omega = 2 pi f. Omega is always about 6.28 times larger than f in number.
One complete oscillation is treated like one full circle, and one full circle is 2 pi radians. In one time period T the particle covers 2 pi radians, so the angular rate is omega = 2 pi / T. The 2 pi simply converts 'cycles' into 'radians'.
The SI unit of omega is radian per second (rad/s). Hertz is the unit of ordinary frequency f. NCERT states this clearly: omega has unit rad/s, while f (nu) is measured in hertz. Writing omega in hertz is a common NEET mistake.
Omega is simply the number multiplying t inside the sine (or cosine). For example, in y = 2 sin(3x - 40t), omega = 40 rad/s. Then T = 2 pi / omega and f = omega / (2 pi) follow at once.
omega = 2 pi / T = 2 pi f, and f = 1 / T = omega / (2 pi). So if you know any one of omega, T or f, you can get the other two instantly.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
omega = 2 pi / T = 2 pi f, where T is the time period in seconds and f is the frequency in hertz.
Radian per second (rad/s). NCERT notes the word 'radian' is dimensionless, but for clarity the unit is written as rad/s to separate it from frequency in hertz.
Multiply the frequency by 2 pi: omega = 2 pi f. For example, f = 50 Hz gives omega = 2 pi (50) = 100 pi = 314 rad/s.
omega = 2 pi f = 2 pi (50) = 314.16 rad/s. This value appears often in AC and oscillation problems.
Almost every wave and SHM equation, y = a sin(kx - omega t) or x = A sin(omega t), uses omega. Reading omega correctly lets you find T, f, and wave speed v = omega / k in seconds, so many one-mark NEET numericals hinge on it.
