For circular shafts under torsion, the torsion formula (T/J = τ/ρ = Gθ/L) governs the relationship between applied torque, shear stress, and angle of twist, and comparing solid versus hollow (tubular) cross-sections of equivalent torque capacity shows that removing material from the low-stress core near the axis yields a superior strength-to-weight ratio, since shear stress and strain vary linearly with radial distance from the neutral axis. This belongs to mechanics of materials (strength of materials), specifically the theory of torsion in circular members, and extends to shafts of non-uniform diameter and to non-uniform (stepped or gear-loaded) torque distributions along a shaft's length. A related principle relates the mechanical power transmitted by a rotating shaft to the applied torque and angular speed, connecting torsional theory to machine design.
For circular shafts under torsion, the torsion formula (T/J = τ/ρ = Gθ/L) governs the relationship between applied torque, shear stress, and angle of twist, and comparing solid versus hollow (tubular…