# Second Moments of Inertia About the Principal Axes

The second moment of inertia of an object about an axis is the tendency of that object to resist being rotated about that axis. If a sheet of a uniform material were cut out in the shape of the blob, the second moment of inertia would indicate how much inertial resistance the object would have to being rotated on the given axis.

The second moment of inertia of a blob is a measure of how widely spread the blob is from a given axis. The higher the value of the second moment, the more widely spread the blob.

The second moment of inertia of a blob about an axis is computed by taking the weight of each pixel, multiplying it by the square of the distance of that pixel from the given axis, then computing the sum of this value for all the pixels in a blob.

The major axis of a blob is defined as the axis about which the second moment of inertia is the smallest. The major axis of a blob is the axis about which it would be the easiest to spin the blob. The major axis of a blob always passes through the blob's center of mass.

The minor axis of a blob is defined as the axis through the center of mass about which the second moment of inertia is the largest. The minor axis of a blob is the axis about which it would be the hardest to spin the blob. The minor axis of a blob is always a line that is at 90° to the major axis passing through the center of mass.

Together, the major and minor axes are referred to as the principal axes.