A solid cylindrical shaft of radius 5 cm and length 1 m has a shear modulus of 80 GPa. It is twisted by a torque of 2.0×10⁵ N·m. Find the angle of twist in radians.

Step-by-step solution

1. For a solid cylinder, compute polar moment of inertia: $J=\frac{\pi r^4}{2}$.
2. Substitute $r=0.05\text{m}$: $J=\frac{\pi (0.05{)}^4}{2}=9.82\times 10^{-6}{\text{m}}^4$.
3. Use torsion formula: $\theta =\frac{Tl}{JG}$.
4. Substitute $T=2.0\times 10^5\text{N⋅m}$, $l=1\text{m}$, $J=9.82\times 10^{-6}{\text{m}}^4$, $G=8.0\times 10^{10}\text{Pa}$.
5. Compute denominator: $JG=9.82\times 10^{-6}\times 8.0\times 10^{10}=7.86\times 10^5$.
6. Compute numerator: $Tl=2.0\times 10^5\text{N⋅m}$.
7. Divide to obtain $\theta =\frac{2.0\times 10^5}{7.86\times 10^5}=0.2547\text{rad}$.
8. Round to three decimal places: $0.255\text{rad}$.

Concept tested: Angle of twist using shear modulus

Published 10 October 2026 · How this solution was prepared and checked