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Second moment of area. The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an (for an axis that ...
List of moments of inertia. Moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis; it is the rotational analogue to mass (which determines an object's resistance to linear acceleration). The moments of inertia of a mass have units of dimension ML 2 ( [mass] × [length] 2).
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relative to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis.
The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, [1] named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between ...
Simpson's rules are a set of rules used in ship stability and naval architecture, to calculate the areas and volumes of irregular figures. [1] This is an application of Simpson's rule for finding the values of an integral, here interpreted as the area under a curve. Simpson's First Rule.
The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not be confused with the mass moment of inertia.
This is when the body rotates around its axis with the smallest moment of inertia. The tennis racket effect occurs when is very close to a saddle point. The body would linger near the saddle point, then rapidly move to the other saddle point, near , linger again for a long time, and so on. The motion repeats with period .
Planar lamina. In mathematics, a planar lamina (or plane lamina[1]) is a figure representing a thin, usually uniform, flat layer of the solid. It serves also as an idealized model of a planar cross section of a solid body in integration. Planar laminas can be used to determine moments of inertia, or center of mass of flat figures, as well as an ...