![]() ![]() In these figures, we assume that the solids are of uniform density throughout. If we rotate that same rod about one of its ends, the moment of inertia is: The moment of inertia of a cylindrical rod thin enough that its width is a small fraction of its length, and rotating about its center of mass, is They rely on integral calculus, and I won't present their derivations here. The moments of inertia of more complicated objects are more difficult to compute. The moment of inertia of the two-mass system shown isĪnd in general, the moment of inertia of n masses in a line, where the r i are the distances from the center of mass, is the sum: The moment of inertia of two masses connected by a mass-less rod is the sum of the masses multiplied by the square of the distance between each mass and the center of mass. ![]() The first moment of the distribution is the sum of all measurements divided by the number of measurements, or the mean (or average). ![]() It could represent any group of experimental measurements of some value, such as a length, a mass or a temperature. Here is the familiar Gaussian (bell-shaped curve) distribution. The moment of inertia describes how mass is distributed in a rotating object. A distribution can be a probability distribution or (often) a mass distribution. In mathematics, the word moment is a measure – or one of a set of measures or properties – that describe the shape of some distribution. In the physics sense, it doesn't mean "a bit of time." But before we do that, it might help to learn a bit about the concept of a " moment" in mathematics. Our goal in this section is to learn about a specific aspect of rotational motion, the moment of inertia. ![]()
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