Introduction

Definition: Rigid Body

A rigid body is one that does not deform during its motion. The distance between any two points in the rigid body remains fixed.

Idea: Angles to Describe Rotation

In order to completely describe the rotation of a rigid body about a fixed axis, O , it is sufficient to give the angle, $\theta$ , between the position vector of any point in the rigid body (for example the point P in the Fig. 7.1), and some arbitrary, fixed reference line.

  

Figure 7.1: Rotation of a Rigid Body about the axis O

Definition: Radian

The angle $\theta$ expressed in radians is defined as the ratio of the arc length, s , swept out by the angle, to the radius, r , of the corresponding circle:

$$\theta {s\over r}$$ (1)

Note: For a complete revolution, s = 2$\pi$r is the circumference, so that the conversions between revolutions, radians and degrees are given by:

$$\pi$$ (2)

Thus

$$\pi$$ (3)