# Added moment of inertia for cylinder

Discussion in 'Boat Design' started by floating, Mar 2, 2011.

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### floatingJunior Member

For a cylinder rotated underwater about a line perpendicular to its axis (end over end), what is the coefficient of the added moment of inertia? I've only found values for a cylinder rotating about its main axis (which is zero).

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### pamamJunior Member

The moment of inertia for a cylinder rotating about its main axis is NOT 0. The easiest way to find out what you are looking for is to find the mean radius of the cylinder i.e. lenght/2 if it is rotating around one end, then square the radius and multiply by the mass of the cylinder (basically weight/acceleration of gravity (32 ft/sec/sec). This should be close.

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### floatingJunior Member

Sorry, I should have been more clear! The "added" moment of inertia is jargon for the inertia of the water that moves when the cylinder is spun in water. When the cylinder is spun about its long axis, no water mass moves with it if you ignore skin friction, so the added moment of inertia is zero. But when the cylinder is spun end over end, some water moves with it. I am looking for a simple relation that describes how to calculate the moment of inertia of this entrained water.

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### jehardimanSenior Member

The mass moment of rotational inertia you are looking for (slugs-ft^2 for rotational inertia G) is effectively equal to the mass of the cylinder times mass moment radius of gyration squared, which is the same as the normal rotational mass moment of inertia. The added mass of any cylinder when moving perpendicular to the deleloped axis is 1, this is just an extension of that case.

FWIW, this added mass IS NOT entrained water, it is the "jerk" (i.e. v triple dot) of the fluid flow around the body. Entrained water is water totaly contained by a body and subject to acceleration but not included in the buoyancy envelope.

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