Conceptual Dynamics - Independent Learning

Mass Moments

 

Is the area moment of inertia (I), used in strength of materials analysis, and the mass moment of inertia (I) the same? If not, what are their differences?

 



 

 

 

 

 

Mass moment of inertia for a system of particles

 

Mass moment of inertia of a single particle

 

IO = mr2

 

 

Mass moment of inertia of a system of particles

 

IO = ∑miri2

 

 

Mass moment of inertia for a rigid body

 

If we think of a rigid body as a collection of infinitesimally small particles, the mass moment of inertia becomes the integral form of the mass moment of inertia for a system of particles.

 

IO = ∫ri2 dm

 

 

Notice that the mass moment of inertia tables in Appendix A of the book give values of the inertia with respect to a specific axis. What if the axis given is not the one we need? How do we calculate I with respect to a different axis?

 




 

 

 

 

 

Radius of gyration

 

It is often the case that a body’s mass moment of inertia with respect to an axis is expressed in terms of its radius of gyration (k) with respect to that axis.

 

I = mk2