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

0:00 – Mechanics of Solid Lecture Series
0:09 – Outlines on the Session
1:27 – Statement of Perpendicular Axis Theorem
3:25 – Proof of Perpendicular Axis Theorem

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

The perpendicular axis theorem is a formula that relates the moment of inertia of a planar object about an axis perpendicular to its plane to the sum of its moments of inertia about two perpendicular axes lying in its plane.

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 of the object about two perpendicular axes lying in its plane and intersecting at the point where the perpendicular axis passes through the object:

I_z = I_x + I_y

where I_x and I_y are the moments of inertia of the object about the two perpendicular axes in its plane, and I_z is the moment of inertia of the object about the perpendicular axis passing through the point where the other two axes intersect.

The perpendicular axis theorem is useful in physics and engineering, where it is often necessary to calculate the moment of inertia of objects with complex shapes. By breaking down the object into simpler shapes and using the perpendicular axis theorem to calculate their moments of inertia about the perpendicular axis, the total moment of inertia of the object about that axis can be calculated. The perpendicular axis theorem is particularly useful for objects with symmetry, as it allows the moment of inertia about an axis perpendicular to the plane of symmetry to be easily calculated from the moments of inertia about two perpendicular axes lying in the plane of symmetry.