When looking at moment integrals, there are number of different types of moment integrals. Finding the mass moment of inertia, indicating a body’s resistance to angular accelerations.Finding the polar area moment of inertia for a shaft cross section, which will be one factor in that shaft’s resistance to torsion.Finding the area moment of inertia for a beam cross section, which will be one factor in that beam’s resistance to bending.Finding the centroid (geometric center) or center of mass for 2D and 3D shapes.Finding point loads that are equivalent to distributed loads (the equivalent point load).Some of the applications of moment integrals include: Because moments are generally a force times a distance, and because distributed forces are spread out over a range of distances, we will need to use calculus to to determine the net moment exerted by a distributed force.īeyond the most literal definition of a moment integral, the term ‘moment integral’ is also general applied the process of integrating distributed areas or masses that will be resiting some moment about a set axis. Here is a table summarizing the three types of inertia:Ī moment integral, as the name implies, is the general concept using integration to determine the net moment of a force that is spread over an area or volume.

“bird” Source: Sandro Halank (2020_Winter_Youth_Olympics)_by_Sandro_Halank%E2%80%93668.jpg We will talk more about mass moment of inertia in the next sections. An inertia is a quantity of how mass is distributed around a body, such as an ice skater spinning with their arms in or spread out.

An object with a really big inertia is hard to rotate, hence it resists rotation. A really heavy object is hard to move, hence it resists motion. Mass moment of inertia is the rotational equivalent to mass. Product moment of inertia is a shaft’s resistance to torsion (or twisting). The unit is m 4 or ft 4. For this course, you need to know the names of three types of moment of inertia (MOI), when to use each, and the units for each.Īrea moment of inertia is used in structures to determine how stiff a beam is, or how much it will deflect. In this course, when we talk about inertia, we usually refer to mass moment of inertia.

Moment of inertia formula statics