A runner of mass 54.0 kg runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 3.10 m/s. The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.150 rad/s relative to the earth. The radius of the turntable is 2.80 m, and its moment of inertia about the axis of rotation is 85.0 kg*m2.Find the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can treat the runner as a particle.)answer in rad/s please

Explanation:

Angular speed of the turntable is = -0.150 rad/s.

Radius of the turntable is R = 2.80 m  

Moment of inertia of the turntable is I = 85

Mass of the runner is M = 54 kg

Magnitude of the runner's velocity relative to the earth is = 3.10 m/s.

Now, according to the law of conservation of angular momentum

And, the final angular speed of the system is

         =            

         =

         = 0.896 rad/s

Thus, we can conclude that  the final angular velocity of the system if the runner comes to rest relative to the turntable is 0.896 rad/s.

         = 0.611 rad/s

layer a is the exosphere and layer b is the thermosphere.   is the answer i think but i hope this .

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