Best Answer

In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.

Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]

This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.

If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:

Q: State and prove perpendicular axis and parallel axis theorem?

Write your answer...

Submit

Still have questions?

Related questions

the moment of inertia of a body about a given axis is equal to the sum of its moment of inertia about a parallel axis passing through its centre of mass and the product of its mass and square of perpendicular distance between two axis Iz=Ix+Iy

The perpendicular axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two perpendicular axes lying in the plane of the object and intersecting the first axis. This theorem can be proven using the parallel axis theorem and considering the individual moments of inertia about each axis. The perpendicular axis theorem is commonly used to find the moment of inertia of thin planar objects.

I will give a link that explains and proves the theorem.

..?

Postulates are assumed to be true and we need not prove them. They provide the starting point for the proof of a theorem. A theorem is a proposition that can be deduced from postulates. We make a series of logical arguments using these postulates to prove a theorem. For example, visualize two angles, two parallel lines and a single slanted line through the parallel lines. Angle one, on the top, above the first parallel line is an obtuse angle. Angle two below the second parallel line is acute. These two angles are called Exterior angles. They are proved and is therefore a theorem.

Show that corresponding angles are congruent?

Yes, the corollary to one theorem can be used to prove another theorem.

If the lines have the same slope but with different y intercepts then they are parallel

(cos0 + i sin0) m = (cosm0 + i sinm0)

Theorem 8.11 in what book?

You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.

asa theorem