The wagon wheel is the same as a paper plate from example one with several dots around the perimeter (wheel spokes) instead of one. If you watch a movie with a stage coach, the wagon wheels appear to move backwards once a certain speed is reached. The most common example comes from old westerns.
The same thing happens when a digital measurement device does not sample a signal often enough. Look every 75 seconds and the plate appears to be rotating opposite to its true rotation. Every 30 seconds and it becomes difficult to determine the rotation of the plate (this is the NYQUIST FREQUENCY). If you open your eyes every 15 seconds and observe the dot, you can still measure direction of rotation and speed. If the disk began rotating at one revolution per minute, you could observe the angular velocity by looking at it. Imagine a disk (or paper plate) with a dot near the edge.
It is perhaps best explained through example. Aliasing occurs when a system is measured at an insufficient sampling rate.
