Which way to rotate a coin? 
The picture shows rotation of a coin in two ways along a axis passing through the centre of gravity.Which method is easier to rotate the coin?
 A: The perpendicular axis theorem states that, (after defining an x, y, and z axis) the sum of rotational inertias around any two axes chosen is equal to the axis not chosen. In formula:
Ix = Iy + Iz. Define the y-axis to be axis 2 in your diagram. Then define the z-axis to along the diameter of your circle but perpendicular to axis 2. Continuing upon these defintions, axis 1 must be the x-axis. Since rotations along the y-axis and z-axis are identical, the rotational inertias along these axes are the same: Iy = Iz. Therefore Ix = 2Iy, and the rotational inertia along the x-axis (or axis 1) is 2x greater than the rotation inertia along the y-axis (axis 2) and it is more difficult to rotate along axis 1.
Important Note: The perpendicular axis theorem assumes a planar object is being observed. In addition, when using  the formula: Ix = Iy + Iz, the perpendicular axis theorem assumes that the y-axis and z-axis lie within the planar object being observed, and the x-axis is perpendicular to the plane that holds the planar object.
