- #1
Cooojan
Homework Statement
Hi. I ve got a problem, where I have to show torque by integrating the weight of the rod over the whole it's length.
Homework Equations
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Result, what I am suppose to get is:
## \tau_{rod} = \frac{mgb}2 ##
The Attempt at a Solution
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When I try to integrate, I am only getting:
## \tau_{rod} = \frac{mgb^2}2~~~~ ##
I'm sure I'm doing some silly mistake. But why can't I do this:
## \frac{d \tau_{rod}}{db} = mg~b~~~~~~⇒~~~~~~ \int \,d \tau_{rod}= mg \int b\,db~~~~~~⇒~~~~~~ \tau_{rod} = \frac{mgb^2}2~~~~##??
I only get the right answer by doing this:
## \frac{d \tau_{rod}b}{db} = mg~b~~~~~~⇒~~~~~~ \int \,d \tau_{rod}b= mg \int b\,db~~~~~~##
but I don't really understand why should I be doing anything like that, and this seems to me like completely wrong approach.
Im sorry if this seems very stupid :/