![]() ![]() So, our disk looks something like this.Ī disk of small thickness, with a radius of If it has a thickness which is comparable to its radius, it becomes a cylinder, which we will discuss in a future blog. for an annulus, a solid sphere, a spherical shell and a hollow sphere with a very thin shell.įor our purposes, a disk is a solid circle with a small thickness (, small in comparison to the radius of the disk). In upcoming blogs I will derive other moments of inertia, e.g. In this blog, I will derive the moment of inertia of a disk. ![]() ![]() Derivation of the moment of inertia of a disk The moment of inertia about the other two cardinal axes are denoted by and, but we can consider the moment of inertia about any convenient axis. Normally we consider the moment of inertia about the vertical (z-axis), and we tend to denote this by. To find the total moment of inertia of an object, we need to sum the moment of inertia of all the volume elements in the object over all values of distance from the axis of rotation. Where is the perpendicular distance from the axis of rotation to the volume element. The definition of the moment of inertia of a volume element which has a mass is given by In physics, the rotational equivalent of mass is something called the moment of inertia.
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