Is the moment of inertia about any axis passing through the centriod the same?

Question

this moment of inertia is not related to the mass.
it is the second moment of area i'm talking about......

for example take the semicircle the moment of inertia about the centroid parallel to its base(diameter) is= 0.11*r^4

but the moment of inertia about the centroid perpendicular to its base is =(pi*r^4)/8
why is it so?

Answer 1

Why would you expect them to be the same? For example, take a cylinder of small radius but long length; the moment of inertia around the axis is small, because all parts of the cylinder are close to the axis. However, the moment of inertial about any end is much larger because of the large contribution of the distant parts.

Answer 2

Moment of inertia (or second moment of area, as it is sometimes called) can be thought of as a stength and deflection factor related to direction of load. As I increases, the shape is stronger and deflection is less.

The moment of inertia for the shape you have described will have different values depending on the axis you are considering and the direction of the load.

Answer 3

the three axis in area interior the path of the middle of mass: one alongside the plenty without inertia... (r<<<

Answer 4

apply pappus theorem conveniently to get the clarification about moment of area of semicircular area and quadrant area about the axis mentioned. .