What is perpendicular axis theorem and parallel axis theorem?

This theorem states that the moment of inertia of a planar body about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with the perpendicular axis and lying in the plane of the body.

What is perpendicular axis theorem simple definition?

The perpendicular axis theorem states that the moment of inertia of a planar lamina (i.e. 2-D body) about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point …

What does the parallel axis theorem say?

What is Parallel Axis Theorem? The moment of inertia of a body about an axis parallel to the body passing through its centre is equal to the sum of moment of inertia of the body about the axis passing through the centre and product of the mass of the body times the square of the distance between the two axes.

What is perpendicular axis theorem Quora?

Statement of Perpendicular axes theorem. Moment of Inertia about an axes perpendicular to the plane is equal to the sum of the moment of inertia about two mutually perpendicular axes in the plane of the lamina such that the three axes have a common point of intersection.

How do you prove the perpendicular axis theorem?

M.O.I of a body about an axis passing perpendicularly from it is equal to the sum of the M.O.I of the body about 2 mutually perpendicular axes lying in the plane of the object. md2 = Added M.O.I due to the distance between O and C. This theorem is applicable for any object.

Why do we use perpendicular axis theorem?

Application of Perpendicular Axis Theorem This theorem is most useful when considering a body which is symmetrical about two out of the three axes. If the value of the moment of Inertia about these two axes is known, then we can easily calculate the Moment of Inertia about the third axis by applying this theorem.

When should you use parallel axis theorem?

you generally use that theorem when you know moment of inertia about an axis and are willing to know moment of inertia of an axis parallel to the axis known then this parallel axis theorem is used .

What is parallel axis theorem Quora?

The Parallel Axis Theorem states that a bodies moment of inertia about any given axis is the moment of inertia about the centroid plus the mass of the body times the distance between the point and the centroid squared.

Is perpendicular axis theorem applicable for solid sphere?

If you go through the proof for perpendicular axis theorem, there is a step where you set . This is true only for a planar object in the x-y plane. That is, perpendicular axis theorem doesn’t work for 3D objects because it is derived under the assumption that the object is planar.

How can perpendicular axis theorem and parallel axis theorem be used?

Together, perpendicular axis theorem and parallel axis theorem can be used to simplify the calculations of moment of inertia. They can help us extend our knowledge of the moment of inertia from one axis to other related axes. Thus, we will find it easier to study the rotational dynamics of rigid bodies in various conditions.

How do you find the parallel axis of a rod?

The parallel axis theorem of rod can be determined by finding the moment of inertia of rod. Moment of inertia of rod is given as: I = ML 2. The distance between the end of the rod and its centre is given as: h =. Therefore, the parallel axis theorem of the rod is: I c = ML 2 – M 2. I c = ML 2 – ML 2.

How to find moment of inertia from parallel axis?

The moment of inertia of a body about an axis parallel to the body passing through its centre is equal to the sum of moment of inertia of the body about the axis passing through the centre and product of the mass of the body times the square of the distance between the two axes. Parallel axis theorem statement can be expressed as follows:

Where do the two axes of a plane intersect?

The two axes should intersect where the first axis cuts the plane. Then, we write the perpendicular axis theorem formula as: This theorem can be extremely useful when we know two moments of inertia of a planar object and want to know the third, provided they all are perpendicular.