Composite shaft twist distribution:\nA circular shaft is fixed at A. Segment AB (first half of length) has diameter D; segment BC (second half) has diameter D/2. If the rotation of B relative to A is 0.1 rad, what is the rotation of C relative to B (assume same torque along the shaft)?

Introduction / Context:
Angle of twist under torsion scales with length and inversely with polar second moment J. In stepped shafts, thin segments dominate angular rotation, which is vital for torsional deflection control in drivetrains and tool spindles.

Given Data / Assumptions:

• Shaft fixed at A, torque constant along length.
• AB length = BC length = L/2.
• Diameters: D on AB; D/2 on BC.
• Rotation of B relative to A, θ_AB = 0.1 rad.

Concept / Approach:
Angle of twist: θ = T * L / (G * J). For solid circular shafts, J ∝ d^4. Thus, for equal lengths under same torque, the twist ratio equals the inverse ratio of d^4.

Step-by-Step Solution:

Verification / Alternative check:
Total twist A→C would be 0.1 + 1.6 = 1.7 rad, showing the slender half dominates deflection, as expected.

Why Other Options Are Wrong:

• 0.4, 0.8, 3.2, 0.2 rad do not match the 16× ratio dictated by d^4 scaling.

Common Pitfalls:
Using d^2 instead of d^4; forgetting lengths are equal; mixing up which segment twists more (the thinner segment twists far more).

Final Answer:
1.6 rad