Parallel Axis Theorem is explained and equation is derived with following timestamps:

0:00 – Mechanics of Solid Lecture Series
0:09 – Outlines on the Session
2:07 – Statement of Parallel Axis Theorem
4:30 – Proof of Parallel Axis Theorem

Following points are covered in this video:
1. Statement of Parallel Axis Theorem
2. Proof of Parallel Axis Theorem

Engineering Funda channel is all about Engineering and Technology. Here this video is a part of Mechanics of Solids or Engineering Mechanics.

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Details of Parallel Axis Theorem:

The parallel axis theorem is a formula that relates the moment of inertia of an object about its center of mass to its moment of inertia about a parallel axis that is displaced from the center of mass. It is also known as the Huygens-Steiner theorem or just the parallel axis theorem.

The parallel axis theorem states that the moment of inertia of an object about a parallel axis is equal to the sum of its moment of inertia about its center of mass and the product of its mass and the square of the distance between the two axes:

I = I_cm + md²

where I is the moment of inertia of the object about the parallel axis, I_cm is the moment of inertia of the object about its center of mass, m is the mass of the object, and d is the distance between the two axes.

This formula is useful in physics and engineering, where it is often necessary to calculate the moment of inertia of complex objects or structures. By knowing the moment of inertia of an object about its center of mass and the distance between the center of mass and the desired axis of rotation, the moment of inertia about the new axis can be calculated using the parallel axis theorem. This can be used, for example, to calculate the moment of inertia of a beam about an axis that is displaced from its centroid, which is useful in designing structures that can withstand bending loads without failing.