Angular Displacement

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx² and rotating with angular speed ω (see figure). The value of ω is ______. (neglect friction)

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure.

Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s^–1. The value of n, to the nearest integer, is ________.

In one complete revolution, the disk rotates by 6.28 rad.

Two point masses of mass m₁ = fM and m₂ = (1 - f) M (f < 1) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω₁ for m₁ and ω₂ for m₂. In that case ______.