moment of inertia of a circle with a hole

T, G, and d are all measurable, and g is known.

The equation in the box allows determining the moment of inertia I of any object about any specific pivot point on that object. Figure 2 shows an arbitrary physical pendulum and its theory. You will treat each object as a physical pendulum- any rigid body that swings in a vertical plane about an axis through the body. Now that you have your two objects of identical shape but with different mass distributions, you are ready for the first step in determining their moments of inertia. Figure 1 - 3D printed disk and ring of nearly equal masses Task #2 - Determine the Period for the Disk and Ring Pendulums See Figure 1 for a photo of the two objects alongside an NSTA ruler. When the author of this lesson printed the objects using PLA filament, each of the objects had a mass of about 32 g. In order to keep the masses nearly equal, it was necessary for your teacher to 3D print both objects with 100% infill. The other object will be a ring whose outer radius is also 5', but whose mass is about the same as that of the disk. One of the objects will be a circular disk of radius 5'. Your teacher will provide you with two 3D printed objects. In this lesson you will be comparing the moments of inertia of two objects with identical masses. Task #1 - 3D Print a Planar Disk and Ring with Identical Radii and Masses It should be noted that by the definition, the moment of inertia of a body depends not only on the particular axis on which it rotates, but also on its shape and the way in which its mass is distributed. For continuous rigid objects, the equation would be similar but making use of integrals instead of a sum. The moment of inertia is the sum of the masses of the particles making up the object multiplied by their respective distances squared from the axis of rotation. Moment of inertia can be defined by the equation This is expressed by the equation τ = Iα . By analogy, the moment of inertia of any rigid object is a measure of its resistance to angular acceleration about an axis when a torque is applied to the object. Newton's Second Law of Motion expresses this in the familiar equation F = ma. In addition to being a property of any physical object, mass is a measure of the resistance of an object to acceleration when a net force has been applied to the object. At the heart of these comparisons lie the concepts of mass on one hand and moment of inertia on the other. There are numerous analogies when comparing linear and rotational motion.

Moment of inertia of a circle with a hole