13. Rotational Inertia & Energy
Moment of Inertia of Systems
13PRACTICE PROBLEM
Sometimes, it is advantageous to calculate the moment of inertia with the radius of gyration k. This is defined as the perpendicular distance from the rotation axis at which, if all of the mass of the object is concentrated, the moment of inertia would be the same as the moment of inertia of the actual object. In other words, the moment of inertia of an object is simply I = mk2. In light of this definition, find the radius of gyration of the solid sphere, the hoop, and the solid cylinder in the figure below.
![](https://static.studychannel.pearsonprd.tech/courses/physics/thumbnails/21e7b5ae-c808-4ba6-aa0b-9a7366e8107b)
Sometimes, it is advantageous to calculate the moment of inertia with the radius of gyration k. This is defined as the perpendicular distance from the rotation axis at which, if all of the mass of the object is concentrated, the moment of inertia would be the same as the moment of inertia of the actual object. In other words, the moment of inertia of an object is simply I = mk2. In light of this definition, find the radius of gyration of the solid sphere, the hoop, and the solid cylinder in the figure below.