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Chapter 11

### INTRODUCTION

After completing this chapter, you will be able to:

• Distinguish angular motion from rectilinear and curvilinear motion.

• Discuss the relationships among angular kinematic variables.

• Correctly associate angular kinematic quantities with their units of measure.

• Explain the relationships among angular and linear displacement, angular and linear velocity, and angular and linear acceleration.

• Solve quantitative problems involving angular kinematic quantities and the -relationships between angular and linear kinematic quantities.

Why is a driver longer than a 9-iron? Why do batters slide their hands up the handle of the bat to lay down a bunt but not to drive the ball? How does the angular motion of the discus or hammer during the windup relate to the linear motion of the implement after release?

These questions relate to angular motion, or rotational motion around an axis. The axis of rotation is a line, real or imaginary, oriented perpendicular to the plane in which the rotation occurs, like the axle for the wheels of a cart. In this chapter, we discuss angular motion, which, like linear motion, is a basic component of general motion.

### OBSERVING THE ANGULAR KINEMATICS OF HUMAN MOVEMENT

Understanding angular motion is particularly important for the student of human movement, because most volitional human movement involves rotation of one or more body segments around the joints at which they articulate. Translation of the body as a whole during gait occurs by virtue of rotational motions taking place at the hip, knee, and ankle around imaginary mediolateral axes of rotation. During the performance of jumping jacks, both the arms and the legs rotate around imaginary anteroposterior axes passing through the shoulder and hip joints. The angular motion of sport implements such as golf clubs, baseball bats, and hockey sticks, as well as household and garden tools, is also often of interest.

As discussed in Chapter 2, clinicians, coaches, and teachers of physical activities routinely analyze human movement based on visual observation. What is actually observed in such situations is the angular kinematics of human movement. Based on observation of the timing and range of motion (ROM) of joint actions, the experienced analyst can make inferences about the coordination of muscle activity producing the joint actions and the forces resulting from those joint actions.

### MEASURING ANGLES

As reviewed in Appendix A, an angle is composed of two sides that intersect at a vertex. For purposes of illustration, a simple quantitative kinematic analysis can be achieved by projecting filmed images of the human body onto a piece of paper, with joint centers then marked with dots and the dots connected with lines representing the longitudinal axes of the body segments (Figure 11-1). A protractor can be used to make hand measurements of angles of interest from this representation, with the joint centers forming the vertices of the angles between ...

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