7.13 Parallelopiped

2.1 Pure translational motion
2.2 Pure rotational motion
2.3 Plane motion

3.1 Angular velocity $\omega $
3.2 Angular acceleration $\left( \alpha \right)$
3.3 Kinematics equation for rotational motion
3.4 Analogy between translational motion & rotational motion

6.1 Parallel-axis theorem
6.2 Perpendicular axis theorem

7.1 Thin rod
7.2 Rectangular lamina
7.3 Circular ring
7.4 Circular disc
7.5 Solid cylinder
7.6 Cylindrical shell
7.7 Solid sphere
7.8 Hollow sphere
7.9 Spherical shell
7.10 Solid cone
7.11 Hollow cone
7.12 Hollow hemisphere
7.13 Parallelopiped
7.14 List of moment of inertia $(I)$ and radius of gyration $(K)$ of different bodies

The most simplest form of a geometrical parallelopiped is rectangular parallelopiped as shown in the figure.

Consider a uniform parallelopiped of length $l$ breadth $b$, height $h$ and mass $m$.

Volume of a parallelopiped is, $(V) = lbh$

Mass per unit volume is, $\left( {{\lambda _V}} \right) = \frac{M}{{lbh}}$

As we know that the moment of inertia of a rectangular lamina is, $I = M\left( {\frac{{{l^2} + {b^2}}}{{12}}} \right)$

So, considering infinite rectangular lamina is used to make a rectangular piped. So, the moment of inertia does not change.