Question

The polar moment of inertia of a plane figure about a point is indicative of:

• A. The figure's resistance to bending
• B. The figure's resistance to axial loads
• C. The figure's resistance to torsional deformation
• D. The total area of the plane figure

Hint:

Remember: polar moment of inertia deals with torsion (twisting), while area moment of inertia relates to bending. They are both essential in structural mechanics.

Answer 1

The Correct Option is C

Step 1: The polar moment of inertia \( J \) is a measure of a figure’s ability to resist torsional (twisting) loads. It is calculated about a point—usually the centroid—and is relevant in circular cross-sections and shafts.
Step 2: It is defined as: \[ J = \int\limits_A r^2 \, dA \] where \( r \) is the radial distance from the axis (or point) to a differential area element \( dA \).
Step 3: The larger the value of \( J \), the greater the resistance to twisting. This quantity plays a central role in the torsion formula for circular shafts: \[ \theta = \frac{T L}{G J} \] where \( T \) is torque, \( L \) is length, \( G \) is shear modulus, and \( \theta \) is the angle of twist.
Why the other options are incorrect:

• (A) Bending resistance is related to the area moment of inertia (not polar moment).
• (B) Axial loads relate to area, not moments of inertia.
• (D) Polar moment does not directly reflect total area but how that area is distributed with respect to the axis.