Sunday, 23 March 2014
Parallel Axis Theorem
The moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction in space. The moment of inertia about any axis parallel to that axis through the center of mass is given by |  |
The moment of inertia about Z-axis can be represented as:
Where
Icmis the moment of inertia of an object about its centre of mass
m is the mass of an object
r is the perpendicular distance between the two axes.
Proof:
Assume that the perpendicular distance between the axes lies along the x-axis and the centre of mass lies at the origin. The moment of inertia relative to z-axis that passes through the centre of mass, is represented as
Moment of inertia relative to the new axis with its perpendicular distance r along the x-axis, is represented as:
We get,
The first term is Icm,the second term is mr2and the final term is zero as the origin lies at the centre of mass. Finally,
