Explanation:

The polar moment of inertia is a measure of a shaft's resistance to torsional deformation. The polar moment of inertia is the sum of the moments of inertia of all the infinitesimal elements of the cross-sectional area of the shaft. The polar moment of inertia is denoted by J.

The Torsional Rigidity is the measure of a shaft's ability to resist torsion or twisting. It is the ratio of the polar moment of inertia to the radius of the shaft. The torsional rigidity is denoted by k.

Difference between shaft stiffness and flexural rigidity:

Shaft stiffness is the measure of a shaft's ability to resist bending or deflection under load. It is the ratio of the load applied to the deflection caused by the load. Shaft stiffness is denoted by k.

Flexural rigidity is the measure of a shaft's resistance to bending. It is the product of the modulus of elasticity and the moment of inertia of the shaft's cross-sectional area. Flexural rigidity is denoted by EI.

Torsional section modulus:

The torsional section modulus is a measure of a shaft's ability to resist torsion or twisting. It is the ratio of the polar moment of inertia to the maximum distance from the center of the shaft to the outer surface of the shaft. The torsional section modulus is denoted by Z.

Conclusion:

In conclusion, the ratio of the polar moment of inertia to the radius of the shaft is known as torsional rigidity. It is a measure of a shaft's ability to resist torsion or twisting. The torsional section modulus is another measure of a shaft's ability to resist torsion or twisting. It is the ratio of the polar moment of inertia to the maximum distance from the center of the shaft to the outer surface of the shaft.

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