Angle of twist of a gear relative to another

[fonseh]

Homework Statement

why we need to consider 2 moment caused by the 85Nm in this question ? The question ask for the determine the angle of twist of gear A relative to D .

Homework Equations

The Attempt at a Solution

Why shouldn't the angle of twist = (85)(0.4) / ( (0.5pi)( 0.015^4- 0.01^4)(75)(10^9) ) + (85)(0.25) / (0.5pi)(0.02^4)(75)(10^9) only ?

 

[billy_joule]

I'm not quite sure I understand your question but the factor of 2 you removed is there to account for the fact there are two identical shaft sections, AB and CD.
Without that 2 you're ignoring one of the hollow sections and your answer is the twist of A relative to C (or B relative to D).