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andyrk
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Why can't moment of Inertia be never greater than MR2 for uniform bodies with simple geometrical shapes?
andyrk said:Why can't moment of Inertia be never greater than MR2 for uniform bodies with simple geometrical shapes?
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?
Physically, you could think of transporting every bit of mass of an object to its boundary - what would happen with its moment of inertia?
The moment of inertia is a mathematical representation of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. This means that the moment of inertia will always be equal to or less than MR2, as the square of any number will always be equal to or less than the number itself.
No, moment of inertia can never be greater than MR2. As stated before, the square of any number will always be equal to or less than the number itself. This is a fundamental mathematical principle that applies to the calculation of moment of inertia.
Since moment of inertia is a representation of an object's resistance to changes in its rotational motion, if it were to be greater than MR2, it would essentially mean that the object is able to resist changes in its rotation more than it actually should. This would go against the laws of physics and would not accurately represent the object's rotational behavior.
No, there are no exceptions to this rule. The calculation of moment of inertia is based on fundamental mathematical principles and these principles apply to all objects, regardless of their shape, size, or composition.
Yes, understanding this concept is important in various fields such as engineering, physics, and even sports. For example, in sports like gymnastics and diving, athletes often try to minimize their moment of inertia by tucking their bodies in order to rotate faster. This principle also plays a role in the design of machinery and structures that need to withstand rotational forces.