Question

State the conditions under which
the theorems of parallel axes and
perpendicular axes are applicable. State
the respective mathematical expressions,​

Answer 1

The conditions under which the theorems of parallel axes and perpendicular axes are applicable are as follows :

• Parallel axis theorem can be applied only when the new axis is placed parallel to the geometric axis passing through the centre of mass of that object.

• Perpendicular axis theorem can be applied when the new axis is placed perpendicular to the geometric axis of the object. The new access will be placed on a plane perpendicular to the geometric axis.

Relevant Mathematical Equations :

Parallel axis theorem:

$\boxed{ \rm{I_{new \: axis} = I + m {x}^{2} }}$

Perpendicular axis theorem:

$\boxed{ \rm{I_{z} = I_{x} + I_{y}}}$