# Calculate the inertia tensor of a decomposable object from tensors of the components

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Hi, As we all know we can calculate centre-of-mass positions of an decomposable object by treating the centres of mass of the component objects as particles of mass, thus working out the centre-of-mass by centre-of-mass = Sum( centre_of_mass_of_component x mass ) / total_mass. However I wish to know if there is anything equivalent in calculating the inertia tensor of such an object, of which the sub-components' inertia tensors are known. By doing so I can avoid re-iterating over all small particles again to save a good amount of time. Any ideas are welcome!

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Yes, you can add the component inertia tensors together BUT they have to have been calculated relative to the centre of gravity of the compound. You can find formulae to calculate the inertia tensor around a translated axis - useful if you already calculated the inertia tensor of each component in its own space.

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