Can anyone help me explain how to get x=(L-x) ?. I didn\'t understand this part.

Question

Can anyone help me explain how to get x=(L-x) ?. I didn't understand this part. Thank you!

CALC A slender rod with length L has a mass per unit length that varies with distance from the s of kg/m2. (a) Calculat mass of the rod in terms of y and L. (b) Use Eq. (9.20) to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Use the expression you derived in part (a) to express in terms of M and L. How does your result compare to that for a uniform rod? Explain. (c) Repeat part (b) for an axis at the right end of the rod. How do the results for parts (b) and (c) compare? Explain 9.20)

Explanation / Answer

Because the mass is decreasing as you move along the rod, a little piece of mass is

(dm/dx).dx = Y(L-x).dx

So, if you integrate this mass times the distance from the axis squared (x^2) between 0 and L, you get the moment of inertia.

So we get (L-x) in the integration.

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