![]() 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 trough 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 trough 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. The above table shows the difference between mass moment of inertia and polar moment of inertia.#1 - Ball. ![]() The mass moment of inertia is necessary for the design of components like flywheels of rotary machines, gears, fans, etc. 7] The polar moment of inertia is necessary for the design of rotating components like shafts, coupling, bolts, etc. The mass moment of inertia has a dimensional formula of. 6] The dimensional formula for the polar moment of inertia is. The SI unit for the mass moment of inertia is Kg.m². 5] The polar moment of inertia has an SI unit of m⁴. The equation for the mass moment of inertia is, 4] The equation of the polar moment of inertia is, The mass moment of inertia shows the distribution of mass from the axis of rotation. ![]() 3] The polar moment of inertia shows the distribution of area from the reference axis. The mass moment of inertia depends on the mass of the object and its location from the axis of rotation. 2] The polar moment of inertia depends on the area of cross-section of the object. The mass moment of inertia shows the resistance offered by the object to the change in angular acceleration. Polar moment of inertia Mass moment of inertia 1] The polar moment of inertia shows the resistance offered by the object against the torsional deformation. Polar moment of inertia vs mass moment of inertia: Sr. ![]()
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