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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