How do we describe rotational motion

Assume that you are replacing the bearings in the wheel of your bicycle. To test if you have done a good job, you hold the axle vertically and give it a spin. The axle at the center of the wheel is stationary. The wheel as a whole has no translational motion. But the wheel is turning around the axle. Every point on the wheel undergoes circular motion about an axis of rotation. Such motion around an axis of rotation is called rotational motion.

How do we describe rotational motion?
Assume you make a chalk mark on the rim of the wheel and you originally orient the wheel so that the chalk mark is facing you. This is your reference orientation. The angular position of the wheel describes its orientation relative to this reference orientation. As the wheel rotates, this angular position is changing. The angular displacement measures how far it has rotated from its reference orientation.

It is often convenient to orient a coordinate system such that the z-axis coincides with the axis of rotation and the x-axis defines the reference orientation. Then the angular displacement q of a point P on the wheel is the angle q a line from the axis of rotation to the point P makes with the x-axis.



Angles can be measured in units of degrees or radians. 360 degrees = 2p radians. When describing rotational motion it is most convenient to measure angles in units of radians.