Analytical Mechanics for Students of Physics And Engineering

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The limits of integration are different from those in equation (II) because the independent variable is changed from m to y.
2. Find the moment of inertia about the a;-axis of a lamina which is bounded by the parabola x^ = 2py and the straight line y = a.
Ca) Choosing a horizontal strip for the element of mass we have dm = a •2xdy.
.-. I = 2(7 C yh:dy J = 2aryW2wdy = f (7 a' V^pa.
But m = (J \ 2xdy = ^a a \/2pa.
, .-. 7 = f ma".
(b) We can also take an element of the strip for the element of ma
...ss, in which case we have dm =

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