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Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.

Determine by direct integration the moment of
inertia of the shaded area with respect to the y axis.

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Grade:12th pass

1 Answers

Vikas TU
14149 Points
7 years ago
 
First calculate area by integerating itself,
 A = Int.(4h(x/a – (x/a)^2))  from x = a to x= 0.
    =(4h(x^2/2a – x^3/3a^2)) from a to 0 we get,
    = 4h(a/2 – a/3)
    = 4h(a/3)
    =4ah/3
 
Now moment of inertia let at y distance from x- axis then,
dM = A*y^2dx = >after integration, => Ay^3/3 from y= h to 0 we get,
M = Ah^3/3 
or
M = 4ah*h^3/9 = > 4ah^4/9 Kgm^2.

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