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Question

Find dimension of moment of inertia. Is moment of inertia a vector or scalar?


Solution

We know that the moment of inertia is given by:
$$I=\int { dm }{ R }^{ 2 }$$

So, the dimension of the moment of inertia is:
$$I=\left[ Mass \right] \left[ Length \right] ^{ 2 }$$

$$\left[ Mass \right]$$=$$\left[ M \right] $$ and $$\left[ Length \right] =\left[ L \right] $$

So, $$\left[ I \right]$$$$=\left[ M \right] \left[ L \right] ^{ 2 }$$

Moment of inertia in rotatory motion is equivalent to mass in translatory motion.
As mass is scalar quantity, it is also a scalar quantity.

Physics

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