What Is the Center of Inertia and How Does It Compare to Center of Mass?

[Chemist@]

What is the center of inertia? Is it the same as the center of mass?

 

[Doug Huffman]

What other component of inertia can have space-like - center - dimensions?

 

[Chemist@]

I don't understand.

 

[mathman]

"A https://www.physicsforums.com/wiki/point , near or https://www.physicsforums.com/wiki/within a https://www.physicsforums.com/wiki/body , at which the body's https://www.physicsforums.com/wiki/mass can be https://www.physicsforums.com/wiki/assumed to be https://www.physicsforums.com/wiki/concentrated when considering its rotational motion and https://www.physicsforums.com/wiki/moment_of_inertia . This may be different from its https://www.physicsforums.com/wiki/centre_of_mass which is the equivalent for linear motion."

Above from wikidictionary.

 

[jtbell]

Mathman, all of the links in the body of your text point to nonexistent pages. PF doesn't have a wiki.

 

[Chemist@]

How to calculate it?

 

[mathman]

Mathman, all of the links in the body of your text point to nonexistent pages. PF doesn't have a wiki.

http://en.wiktionary.org/wiki/centre_of_inertia
The above is where I got it.

 

[FactChecker]

Can anyone give an example where it is easy to see that the center of mass is not the center of inertia?

 

[jbriggs444]

As I understand the concept from the rather terse dictionary definition...

Suppose that you have a turntable. On this turntable you have an object. The "center of inertia" of the object is where you could place its entire mass and wind up with the same moment of inertia as the original object.

Suppose, for instance that the object is a thin hoop of mass m, radius r placed flat on the turntable with its center R units from the center of the turntable. The moment of inertia of this hoop with respect to the center of the turntable is $mr^2 + mR^2$.

Its "center of inertia", C, is at distance $\sqrt{r^2+R^2}$ from the center of the turntable so that the moment of inertia works out to $mC^2 = mr^2 + mR^2$

 

[Chemist@]

Shouldn't moment of inertia be used instead of the masses?

 

[dean barry]

Have a look at radius of gyration (mechanics), it assumes all the mass is concentrated at a single point and radius.
For instance a cylinder with a mass of 10 kg and a radius of 0.1 metres, rotating about its longitudinal axis has a moment of inertia of
0.04 kg - m², the radius of gyration = 0.0632 metres

 

[shiromani]

Is center of inertia a valid concept? I think inertia is quantitative concept.