A thin uniform cylindrical turntable of radius 2.2 m and mass 35 kg rotates in a horizontal plane with an initial angular speed of 11 rad/s. The turntable bearing is frictionless. A clump of clay of mass 17 kg is dropped onto the turntable and sticks at a point 1.5 m from the point of rotation.

Find the angular speed of the clay and turntable.

Explanation:

The given data is as follows.

    M = 35 kg,    radius (r) = 2.2 m,

     m = 17 kg,     = 11 rad/s

We assume that will be the final angular speed.

Now, according to the conservation of angular momentum.

or,    

Putting the given values into the above formula as follows.

or,  

      =

      = 7.58 rad/s

Thus, we can conclude that the angular speed of the clay and turntable is 7.58 rad/s.

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