Rotated Section - Moment of Inertia
Rotated Section - Moment of Inertia
(OP)
Hi everybody:
I can see that there are formulas to calculate the moment of inertia of a 2D Area (Second moment of area) here: http://en.wikipedia.org/wiki/Second_moment_of_area
In the same link, there is a formula to calculate the Inertia moments about a ROTATED AXIS (Axis Rotation). But, is there a formula to calculate the Inertia moments of a ROTATED SECTION (rotated area) ??
Thanks in advance.
Eduardo
I can see that there are formulas to calculate the moment of inertia of a 2D Area (Second moment of area) here: http://en.wikipedia.org/wiki/Second_moment_of_area
In the same link, there is a formula to calculate the Inertia moments about a ROTATED AXIS (Axis Rotation). But, is there a formula to calculate the Inertia moments of a ROTATED SECTION (rotated area) ??
Thanks in advance.
Eduardo






RE: Rotated Section - Moment of Inertia
Mike McCann
MMC Engineering
RE: Rotated Section - Moment of Inertia
RE: Rotated Section - Moment of Inertia
RE: Rotated Section - Moment of Inertia
1. You have a 2D Area in a XY axis. You can calculate the Moments of Inertia Ix, Iy, Pxy.
2. You rotate the 2D Area around the origin, with a tetha angle.
3. So, known Ix, Iy, Pxy and tetha: Is there a formula so i can calculate the new Ix, Iy, Pxy around the same axis?
In wikipedia, you can see that there is a way of calculating the Ix', Iy' and Pxy' around the rotated axis, but that is not what i want, because i am not rotating Axis. I am rotating only the 2D Area and i want calculate Ix, Iy, Pxy in the same axis based on the previously Ix, Iy, Pxgy calculated.
Any ideas?
RE: Rotated Section - Moment of Inertia
rotating about the origin is the same as rotating the axes (only in th eopposite direction).
if rotating about the centroid (ie so a square rotates to become a diamond) i suspect you could account for this by using the parallel axis theorem to move the origin to the centroid, rotate the axes (= rotating the shape), and parallel axis theorem again to move from the centroid to the origin
RE: Rotated Section - Moment of Inertia
RE: Rotated Section - Moment of Inertia
The answer is yes, there is and you have found it in the Wikipedia article you quoted earlier. The only thing you must do is change the sign of theta and press on.
BA
RE: Rotated Section - Moment of Inertia
BA
RE: Rotated Section - Moment of Inertia
In the space time continuum rotating the axis is the same as rotating the section in the opposite direction.
That is unless you are down a black hole and then ..who knows!
RE: Rotated Section - Moment of Inertia