A uniformly tapered tube AB of hollow circular cross section is shown in the figure. The tube has constant wall thickness t and length L. The average diameters at the ends are dA and dB = 2dA. The polar moment of inertia may be represented by the approximate formula IP ( (d3 t/4 (see Eq. 3-18).
Derive a formula for the angle of twist ( of the tube when it is subjected to torques T acting at the ends.

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dA