What is human's moment of inertia?

Question

finding its formula

Answer 1

I'm not really sure there is a set-in-stone formula for the moment of inertia of a human. However, you can probably make a good approximation by dividing the human into sections. (I'm assuming you are finding the moment of inertia about the primary axis of the human: from top to bottom.)

It would probably be safe to say the the head and trunk (shoulders to hips) of the human are a cylinder. Well, two cylinders really. Find the moment of inertia for the head and add the moment of inertia for the trunk.

As for the arms and legs, it depends upon their orientation. If the arms and legs are straight up-and-down, you can assume they are part of the trunk, and just make a larger cylinder. If the arms and legs are pointed straight out, you can assume they are rods. Find the moment of inertia for a rod with the axis perpendicular to the length of the rod. Assuming symmetry, the length of the arm "rod" is the length of both arms together, *not* including the width of the trunk (chest). The length of the leg "rod" is the sum of the lengths of the legs.

Hope that gives you a good start!

Answer 2

Moment of inertia, in non-relativistic terms, is simply a point mass (M) times the square of the distance (R^2) perpendicular from the axis of rotation. If we consider your human to be a point mass, then if the body of that human is on a horse of a merry-go-round (carousel) that is R meters from the axis of rotation, your human's moment of inertia would be I = MR^2.

This fundamental formula can be extended to multiple point masses by summing over all points and distances; or through integration if the masses are given as densities within the volume of the body. But I'm guessing you don't want to go there.

Note, moment of inertia is not angular momentum nor momentum; those are horses of a different color that sound alike.

Answer 3

see:
http://en.wikipedia.org/wiki/Moment_of_inertia

You can often approximate MOI using some sort of standard shape:
http://en.wikipedia.org/wiki/List_of_moments_of_inertia