# Where does the plane exist in this parallel axis theorem?

• Benjamin_harsh
In summary, The currents in the two equations, I_AB and I_CD, are equal to the sum of the current through the ground, I_GXX and I_GYY, respectively, plus the product of the area, A, and the square of the respective variables, y and x. The unlabelled rectangular figure represents the area within the plane of the page. It is parallel to the plane and enclosed by four lines.
Benjamin_harsh
Homework Statement
MOI of an area w.r.t any axis in its plane is equal to the MOI of the
area w.r.t a parallel centroidal axis plus the product of
area and square of the distance between the two axes.
Relevant Equations
##I_{AB} = I_{GXX} + A.(y^{2})##

##I_{AB} = I_{GXX} + A.(y^{2})##

Same applies to CD;
##I_{CD} = I_{GYY} + A.(x^{2})##

In the above statement, "any axis in its plane" where does the plane exist in this sketch?

The area is that unlabelled rectangular figure, and it's in the plane of the page.

NascentOxygen said:
The area is that unlabelled rectangular figure, and it's in the plane of the page.
Is that area perpendicular to the plane or parallel to the plane?

Benjamin_harsh said:
Is that area perpendicular to the plane or parallel to the plane?
The area is within the plane. It is that portion of the plane enclosed by four lines.

Benjamin_harsh

## 1. Where does the plane exist in this parallel axis theorem?

The plane exists in the same location as the original object in the parallel axis theorem. The theorem states that the moment of inertia of an object can be calculated by adding the moment of inertia of the object's center of mass and the square of the distance between the object's center of mass and the axis of rotation. Therefore, the plane's location does not change in relation to the original object.

## 2. What is the difference between the parallel axis theorem and the perpendicular axis theorem?

The parallel axis theorem and the perpendicular axis theorem are two different methods for calculating the moment of inertia of an object. The parallel axis theorem applies to objects rotating around an axis that is parallel to the object's axis of symmetry, while the perpendicular axis theorem applies to objects rotating around an axis that is perpendicular to the object's axis of symmetry. The parallel axis theorem is used for calculating the moment of inertia of 2D objects, while the perpendicular axis theorem is used for 3D objects.

## 3. Can the parallel axis theorem be applied to non-uniform objects?

Yes, the parallel axis theorem can be applied to non-uniform objects. The theorem takes into account the object's entire mass and the distance between the center of mass and the axis of rotation, regardless of the object's shape or density. However, the calculation may be more complex for non-uniform objects compared to uniform objects.

## 4. How does the parallel axis theorem affect the rotational motion of an object?

The parallel axis theorem affects the rotational motion of an object by determining its moment of inertia. The moment of inertia is a measure of an object's resistance to changes in its rotational motion. A higher moment of inertia means that it is more difficult to change an object's rotational motion, while a lower moment of inertia means that it is easier to change the object's rotational motion.

## 5. Are there any real-world applications of the parallel axis theorem?

Yes, the parallel axis theorem has several real-world applications. It is commonly used in engineering and physics to calculate the moment of inertia of objects, which is important for understanding an object's rotational motion and stability. The theorem is also used in the design of machines and structures that involve rotational motion, such as gears, flywheels, and bridges.

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