The horizontal side (x-axis) is length 2A and the vertical side (y-axis at x=+-A) is length B. The mass is uniform throughout the sheet so that the center of mass is at the center of the rectangle. What is the moment of inertia for. the rotation around the z-axis at the midpoint of the horizontal side, coordinate (0,0) in terms of A,B and/or mass? The z-axis at the center of mass (hint: use parallel axis)?
I=Icm+mr^2 where Icm is the center of mass moment and r is the distance to center of mass.
The Attempt at a Solution
For part a, the moment of inertia for a point mass is just I=mr^2, so since the center of mass is (B/2) away from the axis, then I=m*(B/2)^2. However, shouldn't we use parallel axis for part a and not part b, in contrary to the hint for part b?
For part b, the moment of inertia would just be zero? This is because lcm=0 as the axis is at the center of mass and r=0 as the point is also at the center of mass, so I=Icm+mr^2=0+m(0)=0.
Is this the correct way to get both or did I miss something?