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.]

A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for rotation on its hinges?

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 through the edge of the disk?

A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ = cx², where x is measured from the center of the rod and c is a constant. Find an expression for c in terms of L and M.

A uniform DVD has mass $m$ and radius $R$. What is its moment of inertia for rotation about an axis perpendicular to its plane and passing through its center?

Consider four uniform objects of equal mass and radius: (A) a solid sphere, (B) a solid cylinder, (C) a thin spherical shell, and (D) a thin ring, all rotating about their central axis. Which moment of inertia is the smallest?

Which of the following factors does the moment of inertia $I$ of an object depend on?

A thin rectangular plate of width $b$ and height $h$ has its left edge along the y-axis and extends from $x=0$ to $x=b$. If the plate has a uniform surface mass density $\rho$, what is the moment of inertia of the plate about the y-axis?