State the difference between second moment of area and second moment of mass
Answers
Answer:
In classical mechanics we assume that the whole mass of body on its centroid/ centre of mass . This holds mainly true in linear motion, where whole body moves with same velocity. The problem arises in motions where different body parts are in different speed. As in case of rotational motion Moment of inertia is the name given to mass in rotation called rotational inertia. Inertia is the rotational analogy of mass. It appears in the relationships for the dynamics of rotational motion.
As in linear motion the moment of inertia must be specified with respect to a chosen axis of rotation (as centroidal or neutral axis or any other specified). For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr2, where m is mass and r radial (joining by a straight line) distance from axis about which moment of inertia is being calculated. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.
The first moment of area equals the summation of area time’s distance to an axis. It is a measure of the distribution of the area of a shape in relationship to an axis.
First moment of area is commonly used in engineering applications to determine the centroid of an object or the statically moment of area.
The second moment of area, also known as moment of inertia of plane area, or second area moment, is a geometrical property of an area which reflects how
its points are distributed with regard to an arbitrary axis. ( similar to how mass was distributed just in this case area ).
It is calculated in the same way , just in case of taking mass here we take an elemental area
.
Here , if we are taking axis in plane of area ( like taking any diameter as an axis ) in case of cylindrical or circular body . We done it by I and call it moment of inertia .
While , if the axis is along any direction perpendicular to plane of area we denote it by J and call it Polar moment of inertia as it seem if we are calculation it around a pole ( centre of circular potion) .
note: Although they all sound confusing but until you try and do some problems. They all will start making sense.