Why can't moment of Inertia be never greater than MR2

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Homework Help Overview

The discussion revolves around the moment of inertia of uniform bodies with simple geometrical shapes, specifically questioning why it cannot exceed the value of MR². The context includes various shapes such as cylinders, spheres, and cubes, with a focus on their physical properties in relation to rolling motion.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of "R" in the context of different shapes, questioning its application to a cube and discussing its relevance to rolling objects. There is an attempt to understand the implications of the moment of inertia formula and its physical interpretation.

Discussion Status

The discussion is ongoing, with participants seeking clarification on definitions and physical concepts. Some have provided mathematical reasoning related to the moment of inertia, while others express confusion about the implications of transporting mass to the boundary of an object.

Contextual Notes

There is a mention of specific conditions related to friction in accelerated pure rolling, which may influence the understanding of the moment of inertia in this context. The original poster's clarification about the meaning of "R" indicates a need for precise definitions in the discussion.

andyrk
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Why can't moment of Inertia be never greater than MR2 for uniform bodies with simple geometrical shapes?
 
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andyrk said:
Why can't moment of Inertia be never greater than MR2 for uniform bodies with simple geometrical shapes?

It's not clear what "R" stands for here. For example, a cube is a simple geometrical shape. What would R be for a cube?
 
TSny said:
It's not clear what "R" stands for here. For example, a cube is a simple geometrical shape. What would R be for a cube?

Apologies. My question was for a condition of friction in Accelerated Pure Rolling of objects like hollow cylinder, solid cylinder, solid sphere, hollow sphere, disc or a ring. So 'R' corresponds to the radius of these objects and 'M' is their mass.
 
The moment of inertia is defined to be ## \int_0^R \rho(r) r^2 dV ##. According to the mean value theorem, that is equal to ## \bar{R}^2 \int_0^R \rho(r) dV = \bar{R}^2 M \le R^2 M ##, where ## 0 \le \bar{R} \le R ##.

Physically, you could think of transporting every bit of mass of an object to its boundary - what would happen with its moment of inertia?
 
I think it grows up, but i don´t understand what´s the concerning
 
Last edited:
Physically, you could think of transporting every bit of mass of an object to its boundary - what would happen with its moment of inertia?

I think it grows up, but i don´t understand what´s the concerning
 

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