9781118230725.pdf

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What Is Physics?

Every mechanical engineer who is hired as a courtroom expert witness to recon-

struct a traffic accident uses physics. Every dance trainer who coaches a ballerina

on how to leap uses physics. Indeed, analyzing complicated motion of any sort re-

quires simplification via an understanding of physics. In this chapter we discuss

how the complicated motion of a system of objects, such as a car or a ballerina,

can be simplified if we determine a special point of the system — the center of

massof that system.

Here is a quick example. If you toss a ball into the air without much spin on the

ball (Fig. 9-1a), its motion is simple — it follows a parabolic path, as we discussed in

Chapter 4, and the ball can be treated as a particle. If, instead, you flip a baseball bat

into the air (Fig. 9-1b), its motion is more complicated. Because every part of the bat

moves differently, along paths of many different shapes, you cannot represent the

bat as a particle. Instead, it is a system of particles each of which follows its own path

through the air. However, the bat has one special point — the center of mass — that

doesmove in a simple parabolic path. The other parts of the bat move around the

center of mass. (To locate the center of mass, balance the bat on an outstretched fin-

ger; the point is above your finger, on the bat’s central axis.)

You cannot make a career of flipping baseball bats into the air, but you can

make a career of advising long-jumpers or dancers on how to leap properly into

the air while either moving their arms and legs or rotating their torso. Your

starting point would be to determine the person’s center of mass because of its

simple motion.

CHAPTER 9

Center of Mass and Linear Momentum

9-1CENTER OF MASS

After reading this module, you should be able to...

9.01Given the positions of several particles along an axis or

a plane, determine the location of their center of mass.

9.02Locate the center of mass of an extended, symmetric

object by using the symmetry.

9.03For a two-dimensional or three-dimensional extended ob-

ject with a uniform distribution of mass, determine the center

of mass by (a) mentally dividing the object into simple geomet-

ric figures, each of which can be replaced by a particle at its

center and (b) finding the center of mass of those particles.

●The center of mass of a system of nparticles is defined to be the point whose coordinates are given by

or

whereMis the total mass of the system.

:rcom

1

M 

n

i 1

mi:ri,

xcom

1

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n

i 1

mixi, ycom

1

M 

n

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miyi, zcom

1

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mizi,

Key Idea

Learning Objectives