The theorem states that "the moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of the moments of inertia of. The principle of parallel axes states that "The moment of inertia of a rigid body about any axis is equal to the sum of its moment of inertia about. The perpendicular-axis theorem for a thin flat plate is well known to be. Ix + Iy = Iz, normal to it. A generalization of this theorem to three-dimensional objects is. Author: Aglae Daniel MD Country: Bangladesh Language: English Genre: Education Published: 3 November 2016 Pages: 495 PDF File Size: 44.64 Mb ePub File Size: 31.94 Mb ISBN: 447-8-75528-728-7 Downloads: 12085 Price: Free Uploader: Aglae Daniel MD Perpendicular axis theorem

The x and y axes for each lamina are parallel but they are off-set from each other and from the x, y axes you are using for the 3D object.

As Triatticus points out, you need to apply the Parallel Axis Perpendicular axis theorem to each lamina. The moment of inertia of a rigid body about any axis is equal to the sum of its perpendicular axis theorem of inertia about a parallel axis through its centre of mass perpendicular axis theorem the product of the mass of the body and the square of the distance between the two axes. So you cannot simply add the moments of inertia MOI for the x and y axes for each lamina.

The x and y axes for each lamina are parallel but they are off-set from each other and from the x, y axes you are using for the 3D object.

The only method is by applying the parallel or perpendicular axis theorem. The theorems not only help us in finding the mass moment of inertia, but also in finding the area moment of inertia perpendicular axis theorem a few perpendicular axis theorem. Thus,these two theorems have wide applications in planar dynamics and helps solving problems in a faster and easier way.

Perpendicular Axis Theorem

The only method is by applying the parallel or perpendicular axis theorem. The theorems not only help us in finding the mass moment of inertia, but also in finding perpendicular axis theorem area moment of inertia with a few changes.

Thus,these two theorems have wide applications in planar dynamics and helps solving problems in a faster and easier way.