# Angle of twist due to linear varying torque

1. Dec 27, 2009

### Dell

in the following question
http://stommel.tamu.edu/~esandt/Teach/Summer00/CVEN305/Examples/Set3/prob3413.jpg

while G and J are parameters and the moment changes by the function M(x)=t*x
i am asked to find the angle of twist from one end to another

i know

dθ/dx=M/(GJ)

therefore

dθ=M/(GJ)dx

dθ=tx/(GJ)*dx

since t,G,J are independant of X

$$\int$$dθ=t/(GJ)$$\int$$xdx from 0 to L

θ=tL^2/(2GJ)

θ=tL^3/(6GJ)

i can see that they have integrated twice, i can only imagine that they integrated once to find the total torque and the second time to find the angle,,,
but surely this should come from the differential equation? surely if M is a function of X and i integrate dx i souldnt need to sum up the torqe seperately??

Last edited by a moderator: Apr 24, 2017