The result is clearly different, and shows you cannot just consider the mass of an object to be concentrated in one point (like you did when you averaged the distance). You'd see that it doesn't come to $\frac MR^2$. The total moment of inertia is just their sum (as we could see in the video): I i1 + i2 + i3 0 + mL2/4 + mL2 5mL2/4 5ML2/12. And also the axis of rotation has its importance. The axis of solid hemisphere about which the moment of inertia has been asked should be parallel to the axis of the disc. One may forget to use the parallel axis theorem while solving such types of questions. And every shape has its different MOI because its weight or mass distribution is different from others. Note: Moment of inertia of a disc is a basic thing applied here and should be remembered. For example, the moment of inertia of a hollow sphere of. r object’s distance from the rotational axis. The result is a formula in terms of the total mass and some linear dimensions of the rigid body. We know the mass is 5 kilograms and the radius is 0.5 meters. (You can verify this by trying to calculate the volume of the sphere using your formula. The equation for finding the moment of inertia is as, Im × r². Step 1: Determine the known values such as the radius and the mass of the sphere. Rotational and periodic motion calculators : Angular Acceleration Calculator. So, the shape that you have described is not a disc at all. $Rd\theta$ is the length of a tiny, tiny arc of radius $R$ and angle $d\theta$ and in the infinitesimal limit it can be approximated to a straight line, that is, a chord but notice that this chord is still not along the z axis (id est, the vertical axis). the electronic sphere would have a definite radius, definite size. However, the thickness of this differential disc is NOT $ R d\theta$ but $Rd\theta cos\theta$. which enter into the formula for the moment of inertia of the electron, i.e. Rod and Solid Sphere Find the moment of inertia of the rod fit butter. The differential mass element in this case is a disc, of radius $r$ where $r = R \cos\theta$ as you have correctly used. Homework Equations Moment of inertia for a solid sphere: Density: Volume of a. The mistake is in the second line, in the calculation of the differential mass element.
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