13. Rotational Inertia & Energy

(II) Determine the moment of inertia of a 19-kg door around its hinges along one side. The door is 2.5 m high and 1.0 m wide. Ignore the thickness of the door.

Figure 10–72 illustrates an H₂O molecule. The O―H bond length is 0.096 nm and the H―O―H bonds make an angle of 104°. Calculate the moment of inertia of the H₂O molecule (assume the atoms are points) about an axis passing through the center of the oxygen atom

(b) in the plane of the molecule, bisecting the H―O―H bonds.

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A crucial part of a piece of machinery starts as a flat uniform cylindrical disk of radius R₀ and mass M. It then has a circular hole of radius R₁ drilled into it (Fig. 10–80). The hole’s center is a distance h from the center of the disk. Find the moment of inertia of this disk (with off-center hole) when rotated about its center, C. [Hint: Consider a solid disk and “subtract” the hole; use the parallel-axis theorem.]

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A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door’s moment of inertia for (b) rotation about a vertical axis inside the door, 15 cm from one edge?