Chapter 14

### INTRODUCTION

After completing this chapter, you will be able to:

• Identify the angular analogues of mass, force, momentum, and impulse.

• Explain why changes in the configuration of a rotating airborne body can produce changes in the body's angular velocity.

• Identify and provide examples of the angular analogues of Newton's laws of motion.

• Define centripetal force and explain where and how it acts.

• Solve quantitative problems relating to the factors that cause or modify angular motion.

Why do sprinters run with more swing phase flexion at the knee than do distance runners? Why do dancers and ice skaters spin more rapidly when their arms are brought in close to the body? How do cats always land on their feet? In this chapter, we explore more concepts pertaining to angular kinetics, from the perspective of the similarities and differences between linear and angular kinetic quantities.

### RESISTANCE TO ANGULAR ACCELERATION

#### Moment of Inertia

Inertia is a body's tendency to resist acceleration (see Chapter 3). Although inertia itself is a concept rather than a quantity that can be measured in units, a body's inertia is directly proportional to its mass (Figure 14-1). According to Newton's second law, the greater a body's mass, the greater its resistance to linear acceleration. Therefore, mass is a body's inertial characteristic for considerations relative to linear motion.

###### FIGURE 14-1

The distribution of mass in a system does not affect its linear momentum.

Resistance to angular acceleration is also a function of a body's mass. The greater the mass, the greater the resistance to angular acceleration. However, the relative ease or difficulty of initiating or halting angular motion depends on an additional factor: the distribution of mass with respect to the axis of rotation.

Consider the baseball bats shown in Figure 14-2. Suppose a player warming up in the on-deck circle adds a weight ring to the bat he is swinging. Will the relative ease of swinging the bat be greater with the weight positioned near the striking end of the bat or with the weight near the bat's grip? Similarly, is it easier to swing a bat held by the grip (the normal hand position) or a bat turned around and held by the barrel?

###### FIGURE 14-2

Although both bats have the same mass, bat A is harder to swing than bat B, because the weight ring on it is positioned farther from the axis of rotation.

Experimentation with a baseball bat or some similar object makes it apparent that the more closely concentrated the mass is to the axis of rotation, the easier it is to swing the object. Conversely, the more ...

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