 Welcome back MechanicalEI, did you know that moment of inertia is a reason why a ship can never sink by pitching? This makes us wonder, what is moment of inertia? Before we jump in check out the previous part of this series to learn about what reactive systems are. Now there are three basic types of moment of inertia. The first one is mass moment of inertia. The mass moment of inertia is a measure of the distribution of the mass of an object relative to a given axis. The mass moment of inertia is denoted by i and is given for say a single particle of mass m as i0 equals r squared m, where line OO is the axis around which one is evaluating the mass moment of inertia and r is the perpendicular distance between the mass and the axis OO. As seen from the above equation, the mass moment of inertia has the units of mass times length squared. The second moment of inertia also known as the area moment of inertia is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of inertia is typically denoted with either an i for an axis that lies in the plane or with a j for an axis perpendicular to the plane. In both cases, it is calculated with a multiple integral over the object in question. Its dimension is length to the fourth power. It is sometimes necessary to calculate the area moment of inertia for a shape with respect to an axis x dash different to the centroidal axis of the shape. However, it is often easier to derive the area moment of inertia with respect to its centroidal axis x and use the parallel axis theorem to derive the area moment of inertia with respect to x dash axis. Parallax's theorem states that area moment of inertia about an axis x dash is equal to the area moment of inertia about the centroidal axis x plus the product of area and the squared perpendicular distance between x and x dash. Third and final type is the polar moment of inertia which is a shaft or beams resistance to being distorted by torsion as a function of its shape. The rigidity comes from the object's cross-sectional area only and does not depend on its material composition. The SI unit for polar moment of inertia like the area moment of inertia is meters to the fourth power and is denoted by J. Hence, we first saw what the mass moment of inertia is then learned about area moment of inertia while looking at the parallel axis theorem and then went on to see what the polar moment of inertia is. Also, thanks a lot for those constructive comments. You helped the channel grow. So here are the top mechanical EIs of our last videos.