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What is the importance of angle of twist?

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From the relation T/J = G.θ/L ;; we have θ = T.L/G.J 

Since G,L,J are constants for a given shaft, 

θ the angle of twist is directly proportional to the twisting moment. 

A shaft, for which the angle of twist is significant, should always be designed or checked for angle of twist in addition to the design stresses in shafts. 

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