A Momentum
Lexical
- (physics) Of a body in motion: the tendency of a body to maintain its inertial motion; the product of its mass and velocity. Momentum - Wikipedia
- The impetus, either of a body in motion, or of an idea or course of events; a moment.
Physics
Moment of Inertia. By definition, the moments of inertia of a differential area dA about the x and y axes are dIx = y2 dA and dIy = x2 dA, respectively, Fig. 10–2. For the entire area A the moments of inertia are determined by integration; i.e.,
Ix
the moment of inertia of the area
is a measure of how the area of a shape is distributed relative to an axis.
It describes how strongly the shape resists bending about that axis.
Area moment of inertia about an axis
( or second moment of area عزم القصور الذاتي للمساحة حول محور أو عزم العطالة للمساحة حول محور Aksialt arealmoment om en akse)
Is a geometric property of an area that describes how the area of a cross-section is distributed relative to an axis. It is defined as the integral of the squared perpendicular distance from the axis over the entire area.
The area moment of inertia about an axis is defined by
\[ I=\int_A r^2dA \]
where (r) is the perpendicular distance from the differential area (dA) to the axis.
For an axis (x), the perpendicular distance is (y), so
\[I_x=\int_A y^2dA\]
Similarly, for an axis (y), the perpendicular distance is (x), so
\[I_y=\int_A x^2dA\]
Thus, the area moment of inertia is obtained by integrating the squared perpendicular distance of each differential area from the axis over the entire area.
Physical Interpretation
The area moment of inertia describes how the area of a cross-section is distributed relative to an axis.
Area located farther from the axis contributes more because the distance is squared. Therefore, moving material farther away from the axis increases the area moment of inertia.
A larger area moment of inertia generally means greater resistance to bending about that axis.
«Important: The area moment of inertia is a geometric property of an area. It is different from the mass moment of inertia, which depends on mass distribution and is used in dynamics.»