![]() The so-called Parallel Axes Theorem is given by the following equation: Editor’s note: The following is an explanation of the inertia test used in the Aug.The moment of inertia of any shape, in respect to an arbitrary, non centroidal axis, can be found if its moment of inertia in respect to a centroidal axis, parallel to the first one, is known. ![]() ![]() Grab a cup of coffee and your thinking cap.ġ8, 2008 issue of VeloNews (and later in the September 2010 issue). You’ll need them both as Lennard busts out the physics. If you move a rigid object in a straight line, it does not matter how its mass is distributed the amount of work to move it will be the same. This is not true if you drive the object by rotating it then, how the mass is distributed plays an important role in how much energy it takes to move it. In the case of a wheel, it is probably obvious that it will take more work to accelerate it if the mass is concentrated out at its edge than at its center. Rotational inertia, or moment of inertia, is the rotational equivalent of mass this is the quantity that we want to measure to see how much energy it takes to accelerate a wheel. We can measure the mass of the wheel easily enough, but it is not necessarily the case that the lightest wheel will have the lowest moment of inertia, or vice versa. ![]() That’s where the torsional pendulum comes in - a device that measures a wheel’s rotational inertia.Įver since I built this torsional pendulum for bicycle wheels and tested the moment of inertia of some wheels in the Jissue of VeloNews, I’ve wanted to provide readers with a full explanation of the physics involved. #Moment of inertia of a circle formula full If we twist the vertically hanging rod to a relatively small angle without a wheel attached, it will twist back and forth rapidly, and we can measure how many times the horizontal rod welded to it oscillates back and forth in a given amount of time. We don’t want to twist so far that we exceed the elastic limit of the rod we want to be well within the range where it springs back and forth in a repeatable manner. #Moment of inertia of a circle formula full. ![]()
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