Rotations
Rotation in simple terms circular movement. This transformation is the practice of rotating or turning an object about a fixed point known as the center of rotation. The center of rotation may be placed anywhere on the cartesian plane including on the outside or even inside of the object itself. Due to it being a fixed point, the center of rotation cannot move during the transformation. The center of rotation may be placed about the same plane as the object but must remain in the same position throughout the transformation. When the rotaion is complete a new center of rotation may be selected, again anywhere about the same plane as the object.
Rotation is also defined as a rigid transformation so if the object's shape or size is altered during this transformation it is not defined as a rotation. This transformation differs from the transformation translation as the orientation of the shap can be altered from the original position to the transformed position.
The washer drum in a washing machine, the turning of a carnival's ferris wheel, the spinning of wheels on bikes, and the earths rotation are all great exmaples of rotation. The ferris wheel does not alter in size or shape as the wheel rotates so it statisfies the definition of the transformation. For each example stated there are center of rotations, for the ferris wheel example the center of rotation is visible as the middle of the wheel.
Through this applet by Jon Ingram, constructed useing the software GeoGebra, we can explore the transformation rotation.
Within this applet what do you notice if you adjust the center of rotation?
Can you find any patterns with this transformation?
Check out this video on rotations for additional exploration!
https://www.youtube.com/watch?v=NhtTKhP3d6s
https://www.youtube.com/watch?v=NhtTKhP3d6s