Polar Moment Of Inertia
Moment of Inertia about the z axis


The Polar Area Moment Of Inertia of a beams crosssectional area measures the beams ability to resist torsion. The larger the Polar Moment of Inertia the less the beam will twist.


The following are the mathematical equations to calculate the Polar Moment of Inertia:

J_{z}


x is the distance from the y axis to an infinetsimal area dA.

y is the distance from the x axis to an infinetsimal area dA.

PERPENDICULAR AXIS THEOREM:

The moment of inertia of a plane area about an axis normal to the plane is equal to the sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis.



Using the PERPENDICULAR AXIS THEOREM yeilds the following equations for the Polar Moment of Inertia:



J_{z} = I_{x}+I_{y}

