Physics · Motion In A Plane · NEET
No. Angular velocity omega is how fast the angle sweeps, in radians per second (rad/s). Linear velocity v is how fast the body moves along the circle path, in metres per second (m/s). They are joined by v = r omega. Two bodies can have the same omega but different v if their radii differ. For NEET, always check whether the question asks for the angle rate (omega) or the path speed (v).
Time period T is the time in seconds to finish one complete revolution. Frequency f is the number of revolutions in one second, measured in hertz (Hz). They are reciprocals: f = 1 / T and T = 1 / f. Example: if T = 4 s, then f = 0.25 Hz. NEET often gives one and expects the other, so this swap must be automatic.
One full circle is an angle of 2 pi radians (360 degrees = 2 pi rad). The body covers this whole angle in one time period T. So angular velocity = total angle / time = 2 pi / T. Since f = 1 / T, we can also write omega = 2 pi f. This single relation, omega = 2 pi / T = 2 pi f, is the core formula for this topic.
Yes. Because omega = 2 pi / T depends only on T, any two bodies with equal time periods have equal angular velocities, no matter their radius or their linear speed. This exact idea was tested in NEET 2019, where the answer was a 1:1 ratio. Do not get distracted by different radii or speeds given in the problem.
Angular velocity is measured in radians per second (rad/s). The radian is dimensionless (it is arc length divided by radius), so the dimensional formula of omega is T raised to the power minus one, that is [T^-1]. Be careful: rpm (revolutions per minute) must be converted using omega = 2 pi N / 60, where N is revolutions per minute, before using it in any formula.
In time T the body travels the full circle, a distance equal to the circumference 2 pi r. So linear speed v = distance / time = 2 pi r / T. Since omega = 2 pi / T, substitute to get v = r omega. This means for a fixed omega, a larger radius gives a larger linear speed. It is one of the most used relations in circular motion questions.
Two particles A and B are moving in uniform circular motion in concentric circles of radii r_A and r_B with speeds v_A and v_B respectively. Their time period of rotation is the same. The ratio of the angular speed of A to that of B is:
A particle moves in a circle of radius 3 m with time period T = 4 s. It starts at t = 0 on the +y axis. The y-projection of its radius vector is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The SI unit is radian per second (rad/s). Since a radian is dimensionless, the dimensional formula is [M^0 L^0 T^-1], often written [T^-1].
If N is revolutions per minute, then omega = 2 pi N / 60 rad/s. Divide by 60 because rpm is per minute and omega is per second, and multiply by 2 pi to convert revolutions to radians.
omega = 2 pi / T = 2 pi f, and f = 1 / T. One full revolution is 2 pi radians, covered in one time period T.
Yes, angular velocity is a vector. Its direction is along the axis of rotation, given by the right-hand rule. In basic NEET numericals it is usually treated as a magnitude in rad/s.
In uniform circular motion the speed and time period are constant, so omega = 2 pi / T is also constant. Only the direction of the linear velocity keeps changing, which produces centripetal acceleration.
