71

Summary

Selected Vocabulary

center of mass....................the balance point of an object

velocity..............................the rate of change of position; the slope of the tangent line on an x-t

graph.

Notation

x........................................a point in space

t........................................a point in time, a clock reading

........................................

“change in;” the value of a variable afterwards minus its value before

.

x.....................................a distance, or more precisely a change in x, which may be less than the

distance traveled; its plus or minus sign indicates direction

.

t......................................a duration of time

v........................................velocity

v

AB....................................................

the velocity of object A relative to object B

Standard Terminology Avoided in This Book

displacement.....................a name for the symbol

.

x.

speed.................................the absolute value of the velocity, i.e. the velocity stripped of any informa-

tion about its direction

Summary

An object’s center of mass is the point at which it can be balanced. For the time being, we are studying the

mathematical description only of the motion of an object’s center of mass in cases restricted to one dimension.

The motion of an object’s center of mass is usually far simpler than the motion of any of its other parts.

It is important to distinguish location, x, from distance,

.

x, and clock reading, t, from time interval

.

t. When

an object’s x-t graph is linear, we define its velocity as the slope of the line,

.

x/

.

t. When the graph is curved,

we generalize the definition so that the velocity is the slope of the tangent line at a given point on the graph.

Galileo’s principle of inertia states that no force is required to maintain motion with constant velocity in a

straight line, and absolute motion does not cause any observable physical effects. Things typically tend to

reduce their velocity relative to the surface of our planet only because they are physically rubbing against the

planet (or something attached to the planet), not because there is anything special about being at rest with

respect to the earth’s surface. When it seems, for instance, that a force is required to keep a book sliding

across a table, in fact the force is only serving to cancel the contrary force of friction.

Absolute motion is not a well-defined concept, and if two observers are not at rest relative to one another

they will disagree about the absolute velocities of objects. They will, however, agree about relative velocities. If

object A is in motion relative to object B, and B is in motion relative to C, then A’s velocity relative to C is given

by v

AC

=v

AB

+v

BC

. Positive and negative signs are used to indicate the direction of an object’s motion.

Summary