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. Point mass m at a distance r from the axis of rotation. 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. 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. 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. 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. What is the moment of inertia of the section for bending around the z-axis? Express your answer to three significant figures and include the appropriate units.#1 - Ball. Value Units Submit Hints My Answers Give Up Review Part Part B Calculate the moment of inertia Once the position of the centroid is known, the moment of inertia can be calculated. What is the distance y from the bottom of the section to the centroid? (Figure 3) Express your answer with appropriate units to three significant figures. Part A Locate the centroid Since the widths of the two flanges are not the same, the centroid is not readily apparent. The beam is subjected to a moment so that the internal moment on the section is about the z-axis. It can also be written in terms of the vertical My distance from the neutral axis, y, O each equation, I is the moment of inertia of the Figure 3 of 3 Consider an I-beam section with unequal flanges (Figure 20, where w 9.5 in. The relationship can be written in terms of the maximum stress, Mc e, where c is the perpendicular distance max from the neutral axis to the farthest point in the section. When a beam is subjected to an internal bending moment M (Figure 1), he stress distribution acting on a cross section can be related to the moment at that section and the geometric properties of the cross section using the flexure formula. Tem 2 Learning Goal: To find the centroid and moment of inertia of an I- beam's cross section, and to use the flexure formula to find the stress at a point on the cross section due to an internal bending moment.

Internal moment of inertia equation