Mass Moment of Inertia and Area Moment of Inertia – Applications, Differences, and Units

The term “moment of inertia” is used very frequently in mechanical design calculations. There are two different types of moment of inertia: mass moment of inertia and area moment of inertia. Sometimes this creates confusion about which moment of inertia is to be used in which place. Understand the concept of the mass moment of inertia and the area moment of inertia, and you won’t have this problem.

Mass Moment of Inertia

Mass moment of inertia (sometimes called just “moment of inertia”) is responsible for providing resistance against changing the rotational speed of a rotating body. The mass moment of inertia is represented by “I” in mechanical and structural design calculations.

The units of the mass moment of inertia are Kg-M², Gram-Cm****², Lb-Inch****² etc.

The general formula for calculating the mass moment of inertia can be given as:

I = ∫ r****² dM………………….1.1

Where,

I – Mass moment of inertia.

dM – A very small mass parallel to the desired axis.

r – Distance of the small area from the axis.

However, you need not to use this equation most of the time as mass moment of inertia values for standard geometries are readily available.

The mass moment of inertia is the rotational analog of mass. That means, in all the rotational equations of angular momentum, angular kinetic energy, force etc. the mass moment of inertia (I) should be used.

Area Moment of Inertia

Area moment of inertia or second moment of area or second moment of inertia is used in beam equations for the design of shafts or similar members. Area moment of inertia is the property of a section. Like mass moment of inertia, area moment of inertia is also represented by “I” but the units of the area moment of inertia are different than that of the mass moment of inertia. The units of the area moment of inertia are m4, mm4, inch4, etc.

The general formula for calculating the area moment of inertia can be given as:

Ixx = ∫ y****² dA………………….1.2

Where,

Ixx – Area moment of inertia about X axis.

dA – A very small area parallel to the X axis.

y – Distance of the small area from the X axis.

However, you do not need to use this equation most of the time as area moment of inertia values for standard geometries are readily available.

Conclusion

The mass moment of inertia and area moment of inertia both are represented by I. Sometimes it may be confusing, but you have to figure it out by the application. The mass moment of inertia is used as a rotational analog of mass, and the area moment of inertia is used mainly for beam equations. The other difference is the units used in both the moments of inertia.