Rotational Motion

Abstract

In this chapter, we first treat the rotation of an extended object about a fixed axis. This is commonly known as pure rotational motion. The analysis is greatly simplified when the object is rigid. To perform this analysis, we first ignore the cause of rotation and describe the rotational motion in terms of angular variables and time. This is known as rotational kinematics. We then discuss the causes of rotation. This is known as rotational dynamics, and through the study of this topic we introduce the concept of torque. After that we treat some general cases where the axis of rotation is not fixed in space. In these cases, rigid bodies can undergo both rotational and translational motion, as in the rolling of objects. 8.1 Radian Measures One radian (1 rad) is the angle subtended at the center of a circle of radius r by an arc of length s equal to the radius of the circle, i.e. s = r, see Fig. 8.1a. Since the circumference of a circle of radius r is s = 2π r, where π 3.14, then 360 • (or one revolution) corresponds to an angle of (2π r)/r = 2π rad, see also Appendix B. Thus: 1 rev = 360 • = 2π rad ⇒ 180 • = π rad (8.1) Therefore: 1 • = (π/180) rad 0.02 rad 1 rad = 180 • /π 57.3 • .