In this figure, point P has an angular position of. Note that every point on the line has the
same angular position: the angular position of a point does not depend on how far that point is
from the origin, O.
We can relate the angular position of P to the length of the arc of the circle between P and the x-
axis by means of an easy equation:
In this equation, l is the length of the arc, and r is the radius of the circle.
Angular Displacement
Now imagine that the wheel is rotated so that every point on line moves from an initial
angular position of to a final angular position of. The angular displacement, , of line
is:
For example, if you rotate a wheel counterclockwise such that the angular position of line
changes from = 45º = /4 to π = 135º = 3 π/4, as illustrated below, then the angular
displacement of line is 90º or π/2 radians.
For line to move in the way described above, every point along the line must rotate 90º
counterclockwise. By definition, the particles that make up a rigid body must stay in the same