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Calculating the moment of inertia (I)

For simple shapes such as squares, rectangles and circles, simple formulas have been worked out and the values must be calculated for each case.

Formula for a circle is Ixx = Iyy equals Pi D to the power 4, where D equals diameter.

Formula for a rectangle is Ixx = bd to the power 3 divided by 12 which equals mm4 and Iyy = bd to the power 3 divided by 12 which equals mm4.

Formula for a square is Ixx = Iyy = bd to the power 3 divided by 12 which equals mm4. For the formula b equals breadth (width) and d equals depth.

Because millimetres are used, large numbers are generated in the calculation.

A standard method of denoting moment of inertia is to write the values as: number x 106106 is a compact way of writing 1,000,000 or 1 million. mm4.

The 106 factor removes unwanted digits from the value.

The calculation is usually worked using four significant figures The number of significant figures is the number of digits used to represent the original number once it has been rounded to the given number of digits, eg 25.0658 is written as 25.07 when rounded to four significant digits. , so some rounding off is required and the decimal point may need to be moved to use the factor of 106.

Example: 73,473,278 mm4 is written as 73.47 x 106 mm4