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

[andyrk]

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

 

[TSny]

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?

 

[andyrk]

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.

 

[voko]

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?

 

[lalo_u]

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

 

[lalo_u]

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