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Two children, 50.0 kg each, sit on opposite ends of a narrow board with length of 4.60 m and mass of 40.0 kg (which can be treated as a thin rod of rotational inertia of 1/12 mL² where L is the length of the board). The board is supported by a pin in the center and the children and board spin in the horizontal plane.

What is the rotational inertia of the board plus children about a vertical axis through the center of the board?

What is the angular momentum (magnitude and direction) of the system if it is rotating with an angular speed of 0.314 rad/s in a clockwise direction as seen from above?

While the system is rotating, the children pull themselves in toward the center of the board until they are 2/3 as far from the center as before. What is the resulting angular speed?

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