What is the difference between second moments of area and the parallel axes theorem ?
The “second moment of area” is more commonly known as the “moment of inertia” and is a resistance to turning about an axis, just as inertia is resistance to movement. The moment of inertia for a small particle is given by the mass of the particle multiplied by the square of the distance of the particle from the axis. The moment of inertia for a large body is given by summing the moments of inertia for all particles of the body. The parallel axes theorem or rule gives you the moment of inertia about an arbitrary axis, given the moment of inertia about a parallel axis through the body’s center of mass. (The moment of inertia about the center of mass is typically easier to calculate). If you know the moment of inertia about the body’s center of mass the moment of inertia of about the parallel axis is given by adding the moment of inertia of a particle weighing the same as the body at the body’s center of mass. Roughly, to turn something about an arbitrary axis, you need to turn it about i
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