Physics 2514Lecture 2

P. Gutierrez

Department of Physics & AstronomyUniversity of Oklahoma

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Clicker

To be or not to be, that is the question, but what is the answer?Please test your clicker by selecting any of the answers below.

A) Yes.B) No.C) What?D) Why?E) Sounds good.

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Goal

The goal of Chapter 1 is to introduce the concepts that arerequired to understand motion in a qualitative manner.

Goals for today’s lecture:Introduction to motion;Qualitative introduction to vectors;Introduction to the variables needed to describe motion;Introduction to velocity.

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Introduction

The universe we live in is one of constant change and motion. Inorder to understand it, we need to find a set of principles andaxioms that are based on observation. These can then be usedto develop theories and models specific phenomena.

Mechanics—The science of motion. It consists of twobranches:

Kinematics— The branch that concerns itself with thestudy of the motion independent of its cause;

Originates with Galileo (1564-1642)Dynamics—The branch that concerns itself with thecause of the motion.

Originates with Newton (1642-1727)Further developed by D’Alembert, Lagrange,Hamilton, Jacobi, . . .

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The Assumptions

In order to discuss motion, any physics for that matter, we needto introduce the assumptions that we make:We will assume, at least for most of this semester, that allobjects can be treated as point particles.A point particle has no size. Later in the semester we will seethat this is correct if the point corresponds to the center of massof the object. For a complete description we will also need toinclude the motion about the center of mass.We will also assume, unless told otherwise, that air resistancecan be neglected.We will assume that relativistic and quantum mechanical effectscan be ignored

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Motion Diagram

Consider film of object in motion, then superimpose frames.

⇒

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Coordinate system

To discuss motion, require a reference point.We use a right handed Cartesian coordinate system:

Measure everything from origin.Measurement given as straight line distance or as distancealong each of 3 perpendicular axis.

PSfrag replacements 3 dimensions 2 dimensions

⇒

Need to order things. (What cones first, second, etc. and howmuch later.)

Define time, which depends on repeatability ofmeasurements.

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Clicker Question

What direction is the car traveling in?A) Left;B) Right;C) Can not tell, need to specify position of the car in each

frame;D) Can not tell, need to specify the time at which each frame

occurs;

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Units & Dimensions

Before continuing we discuss units and dimensions

For mechanics, the only quantities that we need to specifyare time, position (length, distance), and mass.

We will use SI units (Systeme Internationale d’Unites)Time in secondPosition in metersMass in kilograms

All other measured quantities are given in terms of thedimensions of mass, length and time.

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Definitions

Some more definitionsCoordinate system Reference frame relative to whichpositions are measured. The standard reference frameis the Cartesian (rectangular) system with threeperpendicular axis.Vector Mathematical object with magnitude and directionScalar Mathematical object that is represented by asingle number such as time, temperature distance, . . .Position vector Vector of length given by distance fromfixed location to object, its direction points toward object.Position This can be defined as either the position vectoror a set of numbers on a grid

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Vector Properties

PSfrag replacements ⇒

~A

~A

~A

~B

~B

~B

~A+

~B

~A − ~B

2~A

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Motion Diagrams

To define position, set up a coordinate system. Note: thatcoordinate systems are arbitrary and do not affect the physics.

Coordinate system 1

PSfrag replacements

x

y

~r1

t1

Coordinate system 2

PSfrag replacements

x

y

~r1

t1

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Motion Diagrams

Since we are interested in motion, lets consider two positionvectors.

Coordinate system 1PSfrag replacements

x

y

~r1

t1

~r2

∆~rt2

Coordinate system 2PSfrag replacements

x

y

~r1

t1

~r2

∆~r t2

∆~r = ~r2 −~r1 is the displacement vector which is thedifference of two positions vectors. It specifies theseparation between two positions and the direction thedisplacement occurs in ( t2 > t1)

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Average Velocity

We are now ready to define the rate at which an object changesits position in a quantitative manner.

Even more definitionsAverage velocity is the displacement divided by thetravel time.

~vavg =∆~r

∆twith

{

∆~r = ~r2 −~r1

∆t = t2 − t1

}

and t2 > t1

PSfrag replacements

x

y

~r1

t1

~r2

∆~rt2

Constant velocity Displace-ment vector does not changefor equal length time intervals

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Speed

IMPORTANT: Speed and velocity are not the same:

Average Speed is the total distance traveled divided by thetime required to travel the distance

speed =distance

time

Example

PSfrag replacements∆~r

path

In this case path length > ∆~r,the time interval is the same,therefore speed > |velocity||velocity| means the magnitude of the ve-locity.

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Clicker

A ball 12 m from a wall travels toward the wall, bounces off of itand returns to the starting position. The total travel time is 5 s.What is the average speed and average velocity of the red ball?Assume that the ball is a point.

PSfrag replacements12 m

average speed, average velocityA) 0 m/s, 0 m/s

B) 4.0 m/s, 0 m/s

C) 4.8 m/s, 0 m/s

D) 4.8 m/s, 4.8 m/s

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Announcement

Finish reading chapter 1. I will discuss motion and its descriptionusing displacements, velocity, and acceleration during Monday’slecture.Make sure you understand the sections on solving problems(1.7, 1.8) and the section on significant figures and units (1.9).

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