What is parallel axis theorem and to whom it is applied so that it can...
Parallel axis for any area is used to add the two mutually perpendicular moment of inertias for areas. It gives a moment of inertia perpendicular to the surface of the body. That is the moment of inertia perpendicular to the surface in considerance.
View all questions of this test
What is parallel axis theorem and to whom it is applied so that it can...
Understanding the Parallel Axis Theorem
The Parallel Axis Theorem is a fundamental principle in mechanics, particularly in the study of rigid bodies and their rotational dynamics. It allows for the calculation of the moment of inertia of an area (or body) about any axis, given its moment of inertia about a parallel axis that passes through its centroid.
Key Features of the Parallel Axis Theorem
- The theorem states that the moment of inertia (I) about any axis parallel to an axis through the centroid (I_c) can be expressed as:
I = I_c + Ad^2
- Where:
- I = Moment of inertia about the new axis
- I_c = Moment of inertia about the centroidal axis
- A = Area of the section
- d = Distance between the two parallel axes
Application of the Theorem
- The Parallel Axis Theorem is primarily applied in the context of area moment of inertia, particularly for:
- Calculating Moments of Inertia for Areas: It allows engineers to determine how an area behaves when rotated about an axis that is not through its centroid.
- Design Considerations: This theorem is crucial in mechanical and civil engineering for designing beams and structural components, accounting for how loads are distributed.
Why Option 'A' is Correct
- Mutually Perpendicular Moments of Inertia: The theorem can be used to find the total moment of inertia for sections that involve two mutually perpendicular axes. This is particularly significant in applications involving bending and torsion of materials, where understanding the relationship between moments of inertia is essential for predicting structural behavior.
- Focus on Areas: The correct answer is option 'A' because the theorem is specifically tailored for areas, ensuring accurate calculations for moments of inertia in two-dimensional sections, which is crucial in mechanical engineering applications.