In order to find the moment of inertia of the semicircle, we will take the sum of both the x and y-axis. As a result, M.O.I will be half the moment of inertia of a full circle. Because the semi-circle rotating around an axis is symmetric in this case, we consider these values to be equal. Likewise, for the semicircle, the x-axis moment of inertia equals the y-axis moment of inertia. Then, we need to pull out the area of a circle which gives us: Now, the M.O.I relative to the origin, Jo = I x + I y = ¼ πr 4 + ¼ πr 4 = ½ πr 4 To establish the moment of inertia of the semi-circle, we will add the x and y axes.īecause of complete symmetry and uniform area distribution, we know that the moment of inertia relative to the x-axis is equal to that of the y-axis for a full circle. To obtain the value of the moment of inertia of semicircle, initially derive the results of the moment of inertia of a full circle and divide it by two for getting the desired result of that moment of inertia for a semicircle. I = πr 4 / 4 Finding Moment of Inertia of Semicircle
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