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hey guys welcome back in this video we want to find the angle of twist at the free end of this shaft thats being applied that has this torque applied to it youll notice the shaft here has two distinct cross-sectional areas so the way that we do this is we use our angle of twist formula which is equal to the the sum here of all of the parts and the parts are where any of these change so we have t l / jg and each of those has that little i there representing each of the parts so if we look at this were saying that this whole thing is going to be made out of steel so it will have a modulus of rigidity of 77 gigapascal so that is the thats constants grew up the torque the internal torque is going to be constant throughout and the thing thats changing here is is J which is our each of the cross-sectional cross-sections polar moment of inertia so we want to do if we define this section the little section as section 1 and the big section as section 2 then what we want to do is we want t
