Question

What is the unit for moment of inertia ?

Answer 1

Hint: Learn about the quantities used in the SI unit system. Study the definition of moment of inertia and try to obtain its mathematical expression. Then from the SI units of its constituents find the unit of moment of inertia.

Complete step by step answer:
 We know that moment of inertia is a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque. The axis may be internal or external and may or may not be fixed. The moment of inertia, however, is always specified with respect to that axis and is defined as the sum of the products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis.

The expression for moment of inertia can be written as, \[I = \sum\limits_i^N {{m_i}{r_i}^2} \] where, \[I\] is the moment of inertia of the body by an axis, \[\sum\limits_i^N {{m_i}} \] is the total mass of the body and \[{r_i}\] is the perpendicular distance of \[ith\] particle from the axis , \[N\] is the total number of particle in the body. Now, in SI systems of units he basic units are: Meter, Kilogram and Second.

Hence, the unit of moment of inertia is \[kg{m^2}\].

Note: Moment of inertia of a body is an extensive or additive property of the body. For a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis).