13. Rotational Inertia & Energy

(III) Determine the moment of inertia of a uniform solid cone whose base has radius R₀, height L and mass M. The axis of rotation (𝒵) is the symmetry axis perpendicular to the base, Fig. 10–66. [Hint: Think of the cone as a stack of infinitesimally thin disks of mass dm, radius R, and thickness dz.]

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A 12-cm-diameter DVD has a mass of 21 g. What is the DVD’s moment of inertia for rotation about a perpendicular axis (a) through its center?

(III) Integrate to derive the formula for the moment of inertia of a uniform thin rod of length ℓ about an axis through its center, perpendicular to the rod (see Fig. 10–21f).

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?