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A small object with a mass of 1.62 kg is moving with a speed of 290...

A small object with a mass of 1.62 kg is moving with a speed of 290 m/s (with respect to the ground) when it collides with a rod with a mass of 11.99 kg and a length of L m. The rod is initially at rest, in a vertical position, and pivots about an axis going through its center of mass which is located exactly halfway along the rod. The object imbeds itself in the rod at a distance L/4 from the pivot point. As a result, the object-rod system starts rotating together. If the magnitude of the angular velocity (in rad/s) of the rotation (with respect to the ground) immediately after the collision is 7.1 rad/s, what is the length L (in m) of the rod? You may treat the object as a point particle.

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