Determine by direct integration the moment ofinertia of the shaded area with respect to the y axis.
hemanth , 8 Years ago
Grade 12th pass
Mechanics> Determine by direct integration the momen...
1 Answers
Vikas TU
Last Activity: 8 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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