[tex]\huge\mathcal{\fcolorbox{Aqua}{azure}{\red{➳Question}}}[/tex]
[tex]\sf\purple{\leadsto ~➢What ~is~ the~ unit ~and ~dimension ~of ~moment ~of~ inertia??????}[/tex]
[tex]\red{\rule{200pt}{5pt}}[/tex]
[tex]\bold{Thank~you~:)}[/tex]
[tex]\sf\purple{\leadsto ~➢What ~is~ the~ unit ~and ~dimension ~of ~moment ~of~ inertia??????}[/tex]
[tex]\red{\rule{200pt}{5pt}}[/tex]
[tex]\bold{Thank~you~:)}[/tex]
Answers & Comments
The dimensional formula of moment of inertia is given by [M¹L² T⁰]
Where,
And the S.I unit of moment of inertia is kilogram meter square (kg·m²).
Verified answer
Answer:
The moment of inertia is a physical quantity that measures an object's resistance to changes in its rotational motion. It depends on both the mass distribution and shape of the object. The unit of moment of inertia depends on the unit of mass and the unit of length used to describe the shape of the object.
The SI unit of mass is the kilogram (kg), and the SI unit of length is the meter (m). Therefore, the SI unit of moment of inertia is kilogram-meter squared (kg·m^2).
To better understand this concept, let's consider a simple example. Imagine a solid cylinder rotating about its central axis. The moment of inertia of this cylinder depends on its mass and shape. If the mass of the cylinder is represented by the letter "m" and its radius is represented by the letter "r", then the moment of inertia can be calculated using the formula:
I = (1/2) * m * r^2
In this equation, "I" represents the moment of inertia. The factor of (1/2) is specific to the cylinder's shape and is derived from the geometry of a solid cylinder.
In conclusion, the moment of inertia is a measure of an object's resistance to changes in its rotational motion. Its unit is kilogram-meter squared (kg·m^2), and it depends on the mass distribution and shape of the object.
Step-by-step explanation:
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