Moment of Inertia of Different Shapes
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Quarter-Circular Arc | Centroid (x,y)= (2r/π, 2r/π)
MOI= πr/2
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| Semi-Circular Arc | Centroid (x,y)= (0, 2r/π)
MOI= πr
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| Arc of Circle | Centroid (x,y)= (rsinα/α,0)
MOI= 2αr
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| Triangular Area | Centroid (x,y)= (0,h/3)
MOI= bh/3
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| Quarter circular area | Centroid (x,y)= (4r/3π, 4r/3π)
MOI= πr²/2
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| Quarter Elliptical Area | Centroid (x,y)= (4a/3π, 4b/3π)
MOI= πab/4
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| Semi Elliptical Area | Centroid (x,y)= (0, 4b/3π)
MOI= πab/2
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| Parabolic spandrel (y=kx²) |
Centroid (x,y)= (3a/4, 3h/10)
MOI= ah/3
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| General spandrel (y=kx^n) |
Centroid (x,y)= ([n+1)/(n+2)]a,[(n+1)/(4n+2)]h)
MOI= ah/n+1
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| Circular Sector | Centroid (x,y)= (2rsinα/3α,0)
MOI= αr²
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| Rectangle | MOI about centroidal axis(Ix'x',Iy'y')= bh³/12, b³h/12
MOI about axes (Ixx,Iyy)= bh³/3, b³h/3
Polar moment of inertia= Ixx+Iyy
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| Triangle | Ix'x'=bh³/36
Ixx=bh³/12
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| Circle | Ixx= Iyy= πR^4/4
Jo= πR^4/2
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| Semicircle | Ixx= Iyy= πR64/8
Jo= πR^4/2
Ix'x'= 0.11R64
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| Quarter Circle | Ixx= Iyy= πR^4/16
Jo= πR^4/8
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| Ellipse | Ixx= πab³/4
Iyy= πa³b/4
Jo= πab/4(a²+b²)
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Created by:
shraddha9
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