The moment of intertia of the first point is i1 = 0 (as the distance from the axis is 0). Of the second point: i2 = m (L/2)^2 = mL^2/4. Of the third point: i3 = mL^2. The total moment of inertia is just their sum (as we could see in the video): I = i1 + i2 + i3 = 0 + mL^2/4 + mL^2 = 5mL^2/4 = 5ML^2/12.. The moment of inertia, or more accurately, the second moment of area, is defined as the integral over the area of a 2D shape, of the squared distance from an axis: where A is the area of the shape and y the distance of any point inside area A from a given axis of rotation.

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The moment of inertia for a solid circle about an axis through its center is derived from the basic principle that. , where R is the radius of the circle. This formula is a result of integrating the mass elements of the circle, considering their distance from the axis of rotation. For a semi-circle, this formula adjusts to , and for a quarter.. Moment of Inertia is an important geometric property used in structural engineering, as it is directly related to the amount of material strength your section has. Generally speaking, the higher the moment of inertia, the more strength it has and the less it will deflect under load. The Moment of Inertia of a circle, or any shape for that.