Torus with minor radius a, major radius b and mass m with axes of rotating going through its center: perpendicular to the major diameter and parallel to the major diameter. Solid and hollow, regular tetrahedron (four flat faces) of side s and mass m with axis of rotation going through its center and one of vertices. Spherical shell of inner radius r₁, outer radius r₂, and mass m with axis of rotation going through its center. Hollow sphere of radius r and mass m with axis of rotation going through its center. Rod of length L and mass m with two axes of rotation: about its center and one end. Solid right circular cone of radius r, height h, and mass m with three axes of rotation passing through its center: parallel to the x, y, or z axes. Hollow right circular cone of radius r, height h, and mass m with three axes of rotation passing through its center: parallel to the x, y, or z axes. Plane regular polygon with n vertices, radius of the circumscribed circle R, and mass m with axis of rotation passing through its center, perpendicular to the plane. Thin rectangular plate of length l, width w, and mass m with axis of rotation going through its center, perpendicular to the plane. If the total mass of kg were concentrated in the sphere, the moment of inertia would be. It may be instructive to compare this moment of inertia with that of a rod or sphere alone.
Point mass m at a distance r from the axis of rotation. The composite moment of inertia is given by the sum of the contributions shown at left. Solid and hollow, regular octahedron (eight flat faces) of side s and mass m with axis of rotation going through its center and one of vertices. Moment of Inertia Calculation 2023 - Structural Basics WebMultiple. An isosceles triangle of mass m, vertex angle 2β, and common-side length L with axis of rotation through tip, perpendicular to plane. Solid and hollow, regular icosahedron (twenty flat faces) of side s and mass m with axis of rotation going through its center and one of vertices. Solid ellipsoid of semiaxes a, b, c, and mass m with three axes of rotation going through its center: parallel to the a, b, or c semiaxes. Solid and hollow, regular dodecahedron (twelve flat faces) of side s and mass m with axis of rotation going through its center and one of vertices. Thin solid disk of radius r and mass m with three axes of rotation going through its center: parallel to the x, y or z axes. Cylindrical shell of radius r and mass m with axis of rotation going through its center, parallel to the height. Cylindrical tube of inner radius r₁, outer radius r₂, height h and mass m with three axes of rotation going through its center: parallel to x, y and z axes. Solid cylinder of radius r, height h and mass m with three axes of rotation going through its center: parallel to x, y and z axes. In integral form the moment of inertia is Ir2dm I r 2 d m. Solid cuboid of length l, width w, height h and mass m with four axes of rotation going through its center: parallel to the length l, width w, height h or to the longest diagonal d. Moments of inertia can be found by summing or integrating over every 'piece of mass' that makes up an object, multiplied by the square of the distance of each 'piece of mass' to the axis. Thin circular hoop of radius r and mass m with three axes of rotation going through its center: parallel to the x, y or z axes. Solid ball of radius r and mass m with axis of rotation going through its center.
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