How do I differentiate m(L^2)/16?

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Homework Help Overview

The discussion revolves around the differentiation of the moment of inertia, represented as I = m(L^2)/16, in the context of a physics problem involving two point masses and their separation by a massless rod. The original poster seeks clarification on how to differentiate this expression, particularly regarding the treatment of constants.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss whether m and L are constants or functions of x, which affects the differentiation process. There are attempts to clarify the original problem statement and the need for a diagram. Some participants question the assumptions made regarding the masses and their distances from the axis of rotation.

Discussion Status

The discussion is ongoing, with participants providing guidance on differentiation techniques and the application of the product and chain rules. There is a recognition of the need to clarify the roles of constants and variables in the differentiation process, but no consensus has been reached on the final form of the derivative.

Contextual Notes

Participants note that the original problem involves calculating the moment of inertia about an axis perpendicular to the rod and passing through a specific distance from one of the masses. There is also mention of the need to consider the positions of the masses relative to the axis when calculating the moment of inertia.

  • #31
Yes! Since dL/dx = 0, what do you get for dI/dx?
dI/dx = d/dx(m1x2 - m2(L - x)2) = ?
 
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  • #32
so dI/dx=2m1+2m2(L-x)

?
 
  • #33
Now the second term is correct, but the first one isn't. You had it right before.

Since you're having so much trouble with differentiation, I would advise you to go back and review the basic differentiation rules, especially the product rule and chain rule, and derivative of a constant rule.
 
  • #34
ahh ye just missed the x from the first term
thanks for all the help btw =]
 

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