A thin uniform cylindrical turntable of radius 2.3 m and mass 22 kg rotates in a horizontal plane with an initial angular speed of 7.3 rad/s. The turntable bearing is frictionless. A clump of clay of mass 8.7 kg is dropped onto the turntable and sticks at a point 1.5 m from the point of rotation. Treat the clay as a point mass. Find the angular speed of the clay and turntable. Answer in units of rad/s.

ω = 5.5 rad/s

Explanation:

       where I = moment of inertia regarding the axis of rotation, and ω =

       angular speed of the rotating body.

       where L₀ = I₀ * ω₀,  Lf = If * ωf.

       I₀ is the moment of inertia of a solid disk rotating around an axis

       passing through its center, as follows:

      If, is the moment of inertia after dropping the clump of clay, which adds

      its own moment of inertia as a point mass, as follows:

resonant frequency