A disc of mass M = 2m and radius R is pivoted at its centre. The disc is free to rotate in the vertical plane about its horizontal axis through its centre O. A particle of mass m is stuck on the periphery of the disc. Find the frequency of small oscillations of the system about its equilibrium position.

A disc is free to rotate about a smooth horizontal axis passing through its centre of mass. A particle is fixed at the top of the disc. A slight push is given to the disc and it starts rotating. During the process.

A disc of radius R is pivoted at its rim. The period for small oscillations about an axis perpendicular to the plane of disc is

A disc of radius R is pivoted at its rim. The period for small oscillations about an axis perpendicular to the plane of disc is

A uniform disc of radius a and mass m, is rotating freely with angular speed omega in a horizontal plane about a smooth fixed vertical axis through its centre. A particle, also of mass m, is suddenly attached to the rim of the disc of the disc and rotates with it. The new angular speed is

A uniform disc of radius 'a' and mass 'm' is rotating freely with angular speed omega in a horizontal plane about a smooth fixed vertical axis through its centre. A particle of mass 'm' is then suddenly attached to the rim of the disc and rotates with it. The new angular speed is

One end of a metal rod of length L and mass M is pivoted to a fixed support and to its free end, a thin disc of mass m and radius r (L) is attached at its centre. In one case, the disc is attached to the rod in such a way that it is not free to rotate about its centre and in another case, teh disc is free to rotate about its centre. When the rod-disc system is displaced slightly from its equilibrium position and released. it peforms S.H.M. in vertical plane. Compare the restoring torque acting on the system and angular frequency in both the cases.