If torsional rigidity increases in the torsion equation, then the:

Concept:

We use the torsion equation to analyze the relationship between torsional rigidity and angle of twist in a shaft under torque.

Given:

• Torsion equation: \(\frac{T}{J} = \frac{G \cdot \theta}{L}\)
• Torsional rigidity: \(G J\)
• Angle of twist: \(\theta\)

Step 1: Rearrange the torsion equation

To express angle of twist explicitly:

\(\theta = \frac{T L}{G J}\)

Step 2: Analyze the relationship

The equation shows:

\(\theta \propto \frac{1}{G \cdot J}\)

This means:

• When torsional rigidity (\(G J\)) increases, angle of twist (\(\theta\)) decreases
• When torsional rigidity decreases, angle of twist increases

Step 3: Physical interpretation

Torsional rigidity represents a shaft's resistance to twisting:

• Higher \(G J\) (stiffer shaft) → Less twist under same torque
• Lower \(G J\) (more flexible shaft) → More twist under same torque

Increasing torsional rigidity decreases the angle of twist in a shaft under torsion.