Search
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/37%3A__Moment_of_Inertia/37.02%3A_Radius_of_GyrationA quantity closely related to the moment of inertia is the radius of gyration k. Whatever the shape of a body, if all its mass were to be located at the radius gyration k, then the moment of i...A quantity closely related to the moment of inertia is the radius of gyration k. Whatever the shape of a body, if all its mass were to be located at the radius gyration k, then the moment of inertia would be unchanged. where I is the moment of inertia and m is the mass of the body. As with moment of inertia, the radius of gyration depends upon the axis about which the body is rotated.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/16%3A_Hydrostatics/16.06%3A_Centre_of_PressureIf you were to replace all of these forces by a single force such that the (first) moment of this force about a line through the surface of the fluid is the same as the (first) moment of all the actua...If you were to replace all of these forces by a single force such that the (first) moment of this force about a line through the surface of the fluid is the same as the (first) moment of all the actual forces, where would you place this single force? You would place it at the centre of pressure.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Heat_and_Thermodynamics_(Tatum)/04%3A_Thermal_Conduction/4.01%3A_Error_FunctionThe maximum value, which occurs at x = 0, is 1/√π=0.5642, and it is easy to show that the half width at half the maximum is √ln2=0.8326. Also of some interest (though n...The maximum value, which occurs at x = 0, is 1/√π=0.5642, and it is easy to show that the half width at half the maximum is √ln2=0.8326. Also of some interest (though not particularly in this chapter) is the square root of the second moment of area around the y-axis. The area outside the limits x = ±a, which is the area under the two “tails” of the gaussian function, is sometimes called the complementary error function:
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/02%3A_Moments_of_Inertia/2.04%3A_Radius_of_GyrationThe second moment of inertia of any body can be written in the form mk², where k is the radius of gyration. If all the mass of a body were concentrated at its radius of gyration, its moment of inert...The second moment of inertia of any body can be written in the form mk², where k is the radius of gyration. If all the mass of a body were concentrated at its radius of gyration, its moment of inertia would remain the same.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/02%3A_Vectors_and_Math_Review_Topics/2.08%3A_Math_Review_of_Other_Topics/2.8.24%3A_Calculating_Centers_of_Mass_and_Moments_of_Inertiathe centroid of a region is the geometric center of the region; laminas are often represented by regions in the plane; if the lamina has a constant density, the center of mass of the lamina depends on...the centroid of a region is the geometric center of the region; laminas are often represented by regions in the plane; if the lamina has a constant density, the center of mass of the lamina depends only on the shape of the corresponding planar region; in this case, the center of mass of the lamina corresponds to the centroid of the representative region
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/37%3A__Moment_of_Inertia/37.03%3A_Parallel_Axis_TheoremThe parallel axis theorem (sometimes called Steiner's theorem) relates the moment of inertia Icm about an axis A passing through the center of mass to the moment of inertia I a...The parallel axis theorem (sometimes called Steiner's theorem) relates the moment of inertia Icm about an axis A passing through the center of mass to the moment of inertia I about another axis parallel to A. Using the parallel axis theorem, find the moment of inertia of a rod of mass M and length L about an axis perpendicular to the rod and passing through one end.
