Back(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.
Calculate by direct integration the moment of inertia for a thin rod of mass M and length L about an axis located distance d from one end. Confirm that your answer agrees with Table 12.2 when d=0 and when d = L/2.
(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).
The density (mass per unit length) of a thin rod of length ℓ increases uniformly from λ₀ at one end to 3λ₀ at the other end. Determine the moment of inertia about an axis perpendicular to the rod through its geometric center.