In the first picture, the moment of inertia is being calculated about the base of the figure, which is why sections A, B, and C all have an A ⋅ y-bar2 value added to the MOI of each section about its own centroid.foo9008 said:
normally , the total moment of inertia is I = I(center of mass) + A(d^2) , where d = distance from the centroid of entire mass to the axis,right? why n the 2nd photo , it's I = I(center of mass) - A(d^2)https://en.wikipedia.org/wiki/Parallel_axis_theoremSteamKing said:
In the first page, the moments of inertia of the individual sections A, B, and C are calculated about the individual centroids of A, B, and C, respectively, and then transferred to the base of the by adding Ad2 terms. Once the total inertia is calculated about the base, then the moment of inertia must be corrected to the centroid of the whole figure by subtracting Ad2, where A is the total cross sectional area and d is the location of the centroid w.r.t. the base, in this instance d = 28.07 mm.chetzread said:
cann we just minus the A(d^2) , where a = total area of figure when we are calculating the moment about the centorid of the entire figure ? there's no need to calculate the d one by one just like the author did in the first figure?SteamKing said:
No. Each of the sections A, B, and C is a different area and centroidal location from the reference baseline.chetzread said:
The moment of inertia is a physical property of a rotating object that describes its resistance to changes in its rotational motion. It is dependent on the mass and distribution of the mass around the axis of rotation.
The author may have changed the formula in order to make it more accurate or applicable to a specific situation. They may have also discovered new information or techniques that led to a better understanding of moment of inertia.
The new formula for calculating moment of inertia may vary depending on the specific situation, but it generally involves taking into account the shape, mass, and distribution of the object. It may also involve integration or use of mathematical principles such as the parallel axis theorem or perpendicular axis theorem.
The change in formula may result in a more accurate calculation of moment of inertia, as it takes into account more factors and variables. It may also make the calculation more complex and require more advanced mathematical techniques.
The new formula may not be applicable to all situations, as the moment of inertia can vary depending on the shape and distribution of mass. It is important to use the most appropriate formula for each specific situation in order to get an accurate calculation.
