After completing this chapter, you
will be able to:
- Identify the angular analogues of mass, force, momentum,
- 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 angularkinetics, from the perspective of
the similarities and differences between linear and angular kinetic quantities.
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.
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?
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, ...