HC Verma’s Concepts of Physics – Chapter 10 – Question 15
Find the moment of inertia of a uniform square plate of mass m and edge a about one of its diagonals.
The question was posted by Ankit
Let the moment of inertia about the axis through the centre of the square plate perpendicular to the plane, assumed to be along Z axis, be I. Now the square plate will be in the XY plane. Let the X axis and Y axis be parallel to the edges and passing through the centre.
Then, we know that Ix = Iy = ma2/12
Then, according to perpendicular axis theorem,
Iz = Ix + Iy = 2Ix=2ma2/12=ma2/6
Now, imagine that X and Y axes are along the diagonals. (The diagonals of a square are also mutually perpendicular.)
Again, according to perpendicular axis theorem, Iz = Ix + Iy = 2Ix
The MI about the diagonal about its diagonal, Ix = Iz/2 = ma2/12