The wad of clay of mass m = 0.36 kg is initially moving with a horizontal velocity v1 = 6.0 m/s when it strikes and sticks to the initially stationary uniform slender bar of mass M = 4.3 kg and length L = 1.64 m. Determine the final angular velocity of the combined body and the x-component of the linear impulse applied to the body by the pivot O during the impact. The angular velocity is positive if counterclockwise, negative if clockwise. The impulse is positive if to the right, negative if to the left.

Complete Question

The diagram for this question is shown on the first uploaded image

The angular velocity is  

The linear impulse applied to the body by the pivot O during the impact is

Explanation:

The free body diagram of the image is shown on the second uploaded image

From the question we are told that

     The mass of the wad of clay is  

      Th velocity is  

      The mass of  slender bar

        The length is  

From the diagram  the moment of inertia of the slender bar is

And the moment of inertia of the  slender bar and the clay sticked to it is

According to the law of conservation of angular momentum

    The initial angular momentum =  final angular momentum

The initial angular momentum of the clay is  

The final angular momentum is

 So

So

From the diagram the center of gravity is calculated as

Now angular velocity along the x-axis

Where    is  linear impulse applied to the body by the pivot O

Substituting values

   Making    the subject of the formula

substituting value

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