Chapter 1: Concepts of Motion

Two Types of Models

1. Descriptive Models 2. Explanatory Models

Four Basic Types of Motion

1. Linear 2. Circular 3. Projectile 4. Rotational

Slowing Down Motion Diagram

A *decreasing distance* between the images shows that the object is slowing down

Position-Versus-Time Graph

A continuous line or curve showing an object's position as a function of time. Sometimes just called a position graph

Motion Diagram

A diagram showing an object's position at several equally spaces instants of time. These diagram can be used to define constant speed, speeding up, and slowing down in terms of how they appear on a diagram

Model

A highly simplified picture of reality that still captures the essence of what we want to study

Order-of-Magnitude Estimate

A one-significant-figure estimate or calculation. Indicated by the symbol ~, which indicates even less precision that the "approximately equal" symbol

Vector

A quantity having both a size (the "How far?" or "How fast?") and a direction (the "Which way?")

Scalar

A single number, with a unit, that describes a physical quantity. A scalar can be positive, negative, or zero. Ex: 6 kg

Zero Vector

A vector with zero length

Note on Acceleration

Acceleration refers to changing the velocity, whether it be speeding up or slowing down

Speeding Up Motion Diagram

An *increasing distance* between the images shows that the object is speeding up

Position Vector

An arrow that represents position and goes from the origin to the point we choose. The position vector is given the symbol

Defining Speeding Up and Slowing Down on Motion Diagrams with Displacement Vectors

An object is speeding up if its displacement vectors are increasing in length and slowing down if its displacement vectors are decreasing in length

Particle

An object that can be represented as a mass at a single point in space. Has no size, shape, and no distinction between top and bottom or front and back

Motion in One Dimension

An object's motion can be described in terms of three fundamental quantities: its position, velocity, and acceleration

Average Acceleration

Average acceleration vector points in the same direction as the average velocity vector

Constant Speed Motion Diagram

Images that are *equally spaced* indicate an object moving with constant speed

Average Velocity

In addition to measuring how fast an object moves, this average velocity is a vector that points in the direction of motion

Average Speed

Measures an object's fastness or slowness, defined as the ratio of distance traveled to time interval spent traveling

Translational Motion

Motion in which an object moves through space. Linear, circular, and projectile motion are all translational

Modeling

Stripping away the details to focus on essential features

Motion

The change of an object's position with time

Motion Diagrams with Displacement Vectors

The displacement vectors are simply the arrows connecting each dot to the next. When an object either starts from rest or ends at rest, you should write "Start" or "Stop" to distinguish from slowing down or speeding up

Average Speed with Velocity Vectors

The length of a velocity vector represents the average speed with which the object moves between the two points. Long velocity vectors indicate faster motion

Negative of a Vector

The negative of a vector is a vector with the same length but pointing in the opposite direction

Particle Model

The particle model of motion is a simplification in which we treat a moving object as if all of its mass were concentrated at a single point. Excellent for modeling translation motion of cares, planes, rockets, etc.

Object Trajectory

The path along which the object moves, whether straight or curved

Mechanics

The science of motion

Magnitude of Vector

The size or length of a vector

Full Motion Diagram Example 1.6

The velocity at the top point is changing - from up to down. If the velocity is changing, there must be acceleration and it is not zero. If the ball reached zero velocity at the top, it would hang there and not fall if the acceleration were also zero.

Displacement

This images shows the symbol for an object displacement, which is the change in an object's position

Vector Notation

We indicate a vector by drawing an arrow pointing right over the letter that represents the quantity. The symbols without the arrow represent scalars.

Descriptive Models

What are the essential characteristics and properties of a phenomenon?

Acceleration and Velocity Vectors Direction

When an object is speeding up, the acceleration and velocity vectors point in the same direction. When an object is slowing down, the acceleration and velocity vectors point in opposite directions

Explanatory Models

Why do things happen as they do?

Vector Addition

You can move a vector around on the page as long as you don't change it's length or the direction it points