A heavy disc with radius `R` is rolling down hanging on two non-stretched string wound around the disc very tightly. The free ends of the string are attached to a fixed horizontal support. The strings are always tensed during the motion. At some instant, the angular velocity of the disc is `omega`, and the angle between the strings is `alpha`. Find the velocity of centre of mass of the disc at this moment

Explanation

The velocities of point `A` and `B` being perpendicular to the strings, the instantaneous axis of rotation must be at `D`, instantaneous point of intersection of the line of the two strings.
Therefore,
`V_(CM)=omega.OD=(omegaxxOB)/(cos.(alpha)/(2))=(omegaR)/(cos.(alpha)/(2))`