![]() 'cause this is something that people get confused about a lot. Talk some more about the moment of inertia, You can also check that it would not matter if the distance wasn't squared - then your method would produce correct results. The result is clearly different, and shows you cannot just consider the mass of an object to be concentrated in one point (like you did when you averaged the distance). The total moment of inertia is just their sum (as we could see in the video): I = i1 + i2 + i3 = 0 + mL^2/4 + mL^2 = 5mL^2/4 = 5ML^2/12. The moment of intertia of the first point is i1 = 0 (as the distance from the axis is 0). However, let's now consider these points separately. ![]() One is at the axis of rotation (like the left end of the rod), the third is at the distance L from the axis, and the second point lies exactly between them.Įach has a mass m, so the total mass is obviously M=3m and m = 1/3 M.įollowing your way of thinking, the mean distance from the axis of rotation is L/2 (equal to (0 + L/2 + L)/3), so the moment of inertia would be I am sure you will understand this when you learn calculus, but let me give you an example.Ĭonsider just 3 point masses for simplicity. If there was just L (not-squared), you would be right.
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