Galileo and InertiaGalileo and Inertia

In the early 1600's, the Italian Physicist Galileo Galilee In the early 1600's, the Italian Physicist Galileo Galilee

perfected the concept of modern experimental physics perfected the concept of modern experimental physics

and made one of the most important discoveries in and made one of the most important discoveries in

history. history.

In his experiments, Galileo studied the motion of In his experiments, Galileo studied the motion of

objects by rolling balls down wooden inclined planes.objects by rolling balls down wooden inclined planes.

Galileo and InertiaGalileo and Inertia

Since Galileo knew about friction, he sanded his Since Galileo knew about friction, he sanded his

inclined planes and used water and other lubricants inclined planes and used water and other lubricants

(oils) to reduce the friction. As the friction was (oils) to reduce the friction. As the friction was

reduced, the ball rolled farther.reduced, the ball rolled farther.

Galileo then did something ingenious. He allowed the Galileo then did something ingenious. He allowed the

ball to roll up a second plane!!ball to roll up a second plane!!

Galileo and InertiaGalileo and Inertia

Galileo and InertiaGalileo and Inertia

Regardless of the angle of inclination of the second Regardless of the angle of inclination of the second

inclined plane or its distance from the first inclined inclined plane or its distance from the first inclined

plane, the ball always appeared to roll up the second plane, the ball always appeared to roll up the second

inclined plane until the ball reached its original height. inclined plane until the ball reached its original height.

If the inclined plane was not as steep, the ball would If the inclined plane was not as steep, the ball would

simply roll a greater distance. It was as if the ball simply roll a greater distance. It was as if the ball

somehow remember its starting height!! somehow remember its starting height!!

This discovery was contradictory to Aristotelian This discovery was contradictory to Aristotelian

Mechanics!!Mechanics!!

Galileo and InertiaGalileo and Inertia

Galileo then asked himself a brilliant question!!Galileo then asked himself a brilliant question!!

If the inclined plane had an angle of inclination of zero If the inclined plane had an angle of inclination of zero

(i.e. it was horizontal), when would the ball reach its (i.e. it was horizontal), when would the ball reach its

original height?original height?

Galileo and InertiaGalileo and Inertia

Answer: It would never reach its original height so it Answer: It would never reach its original height so it

would never stop!!would never stop!!

Galileo therefore concluded that the “natural” state of Galileo therefore concluded that the “natural” state of

motion is not rest!!motion is not rest!!

Galileo and InertiaGalileo and Inertia

Galileo knew that the Earth was a sphere and the ball Galileo knew that the Earth was a sphere and the ball

appeared to keep rolling along the surface of the appeared to keep rolling along the surface of the

sphere. He also believed that the planets including the sphere. He also believed that the planets including the

Earth traveled in circular orbits at constant speeds Earth traveled in circular orbits at constant speeds

(uniform circular motion) around the sun.(uniform circular motion) around the sun.

Thus, Galileo decided that all objects continue in Thus, Galileo decided that all objects continue in

uniform circular motion unless a net push or pull (i.e. uniform circular motion unless a net push or pull (i.e.

force is applied) to the object. force is applied) to the object.

Galileo and InertiaGalileo and InertiaThus, Galileo was able to explain why objects don’t fall Thus, Galileo was able to explain why objects don’t fall

off the Earth as it spins on its axis or rotates around off the Earth as it spins on its axis or rotates around

the sun.the sun.

Although Galileo experiments were brilliant, he was Although Galileo experiments were brilliant, he was

incorrect about the natural state of motion since he incorrect about the natural state of motion since he

didn’t know about the concept of gravity. Rene Descart didn’t know about the concept of gravity. Rene Descart

refined Galileo’s work by stating that the natural refined Galileo’s work by stating that the natural

state of motion of an object is a straight line at state of motion of an object is a straight line at

constant speed and not a curved path. The concept of constant speed and not a curved path. The concept of

inertia was given its final form by the great Sir Isaac inertia was given its final form by the great Sir Isaac

Newton as Newton’s 1Newton as Newton’s 1stst Law. Law.

Newton’s 1Newton’s 1stst Law of Mechanics Law of MechanicsA particle will continue is a straight line at constant A particle will continue is a straight line at constant

speed unless acted upon by a net push or pull (i.e. speed unless acted upon by a net push or pull (i.e.

force). force).

The property of a body to continue in a straight line at The property of a body to continue in a straight line at

constant speed is called constant speed is called InertiaInertia..

MassMass is the is the measuremeasure of a of a body’s inertiabody’s inertia. Thus, a 2 kilo-. Thus, a 2 kilo-

gram object has twice the inertia of a 1 kilo-gram gram object has twice the inertia of a 1 kilo-gram

object. object.

Newton’s 1Newton’s 1stst Law of Mechanics Law of MechanicsNewton’s 1Newton’s 1stst Law tells us a couple of things: Law tells us a couple of things:

1)1) The natural state of mater is a straight line at The natural state of mater is a straight line at

constant speed.constant speed.

2)2) If an object is not moving in a straight line and/or if If an object is not moving in a straight line and/or if it is speeding up or slowing down then a net push it is speeding up or slowing down then a net push or pull must be acting upon the body.or pull must be acting upon the body.

Newton’s 1Newton’s 1stst Law LawQuestion 1: Since an apple speeds up as it falls to the Question 1: Since an apple speeds up as it falls to the

ground, what does Newton’s 1ground, what does Newton’s 1stst Law say about the net Law say about the net

push or pull on the apple? push or pull on the apple?

Question 2: When an object is dropped from a very Question 2: When an object is dropped from a very

high place, the object will initially pickup speed until it high place, the object will initially pickup speed until it

reaches some maximum speed (terminal speed) after reaches some maximum speed (terminal speed) after

which its speed stays constant. What does Newton’s which its speed stays constant. What does Newton’s

11stst Law say about the net push or pull on the object Law say about the net push or pull on the object

once it reaches terminal speed?once it reaches terminal speed?

Newton’s 1Newton’s 1stst Law LawQuestion 3: Why does a spaceship need an engine to Question 3: Why does a spaceship need an engine to

blast off from the Earth or land on the moon, but blast off from the Earth or land on the moon, but

not during the trip from the Earth to the Moon?not during the trip from the Earth to the Moon?

Basic Concepts Of MechanicsBasic Concepts Of MechanicsQuestion: How do we describe the location of an Question: How do we describe the location of an

object?object?

Answer: We specify its location in terms of an agreed Answer: We specify its location in terms of an agreed

upon set of directions and by measuring the distance upon set of directions and by measuring the distance

from the object to some reference (possibly a tree).from the object to some reference (possibly a tree).

McDonald’s

South

East

TSU Science Building

Basic Concepts Of MechanicsBasic Concepts Of MechanicsScientist say that you are specifying your coordinate Scientist say that you are specifying your coordinate

axis (i.e. the set of agreed upon directions and your axis (i.e. the set of agreed upon directions and your

origin). In this example, we might designate the origin). In this example, we might designate the

directions x and y as well our reference point (origin) directions x and y as well our reference point (origin)

as the TSU science building.as the TSU science building.

McDonald’s

x

y

TSU Science Building

Basic Concepts Of MechanicsBasic Concepts Of MechanicsThe arrow showing us the location of McDonald’s is The arrow showing us the location of McDonald’s is

called McDonald’s position vector. called McDonald’s position vector.

A vector is a mathematical quantity that has both (size) A vector is a mathematical quantity that has both (size)

magnitude and direction! You must not only tell the magnitude and direction! You must not only tell the

visitor how far it is to McDonald’s, but also the visitor how far it is to McDonald’s, but also the

direction to walk.direction to walk. McDonald’s

x

y

TSU Science Building

600 m

20°

Basic Concepts Of MechanicsBasic Concepts Of MechanicsThe mathematics of vectors is very different from the The mathematics of vectors is very different from the

math of scalars (i.e. regular numbers) which you are math of scalars (i.e. regular numbers) which you are

accustomed to using!! It is not 900 m to Sonic from the accustomed to using!! It is not 900 m to Sonic from the

Science Building nor do you walk towards Science Building nor do you walk towards

McDonald’s!! McDonald’s!!

McDonald’s

x

y

TSU Science Building

600 m20°

Sonic

300 m

Basic Concepts Of MechanicsBasic Concepts Of MechanicsVectors can be added by drawing the vectors to scale Vectors can be added by drawing the vectors to scale

using a ruler and a protractor. This is how explorers using a ruler and a protractor. This is how explorers

Like Columbus charted their course and is still used by Like Columbus charted their course and is still used by

the Navy today!! the Navy today!!

Example:Example: Add the following two vectors using the Add the following two vectors using the

scale 1 cm = 1 m.scale 1 cm = 1 m.

10 m

30°

12 m 120°

Basic Concepts Of MechanicsBasic Concepts Of MechanicsTo simplify the math, we will restrict ourselves in this To simplify the math, we will restrict ourselves in this

course to 1-dimensional problems. Thus, we can course to 1-dimensional problems. Thus, we can

specify the direction of our vectors by the sign of our specify the direction of our vectors by the sign of our

answer. For example, the location of Bruner’s is answer. For example, the location of Bruner’s is

+3000 m and the location of Chamberlain is -1500 m. +3000 m and the location of Chamberlain is -1500 m.

TSU Science

Building

x

Bruner’s

3000 m

Chamberlain

School

1500 m

y

Basic Concepts Of MechanicsBasic Concepts Of MechanicsQuestion: What would be the position vectors for the Question: What would be the position vectors for the

following three locations (Chamberlain, Science following three locations (Chamberlain, Science

building, and Bruner’s) using a coordinate system building, and Bruner’s) using a coordinate system

whose origin was at Chamberlain?whose origin was at Chamberlain?

TSU Science

Building

x

Bruner’s

3000 m

Chamberlain

School

1500 m

y

Basic Concepts Of MechanicsBasic Concepts Of MechanicsNote: The position of an object is not unique!! It always Note: The position of an object is not unique!! It always

depends on your coordinate system. In every problem, depends on your coordinate system. In every problem,

you must first specify your coordinate system and then you must first specify your coordinate system and then

determine the position vector for an object!determine the position vector for an object!

Basic Concepts Of MechanicsBasic Concepts Of MechanicsDisplacement: The displacement of an object is Displacement: The displacement of an object is

defined as the change in the object’s position defined as the change in the object’s position

vector.vector.

Displacement = (Final Position) – (Initial Position)Displacement = (Final Position) – (Initial Position)

Question #1: Using the TSU science building Question #1: Using the TSU science building

coordinate system, calculate a student’s displacement coordinate system, calculate a student’s displacement

if they walk from Chamberlain to Bruner’s. if they walk from Chamberlain to Bruner’s.

Basic Concepts Of MechanicsBasic Concepts Of MechanicsQuestion #2: Using the Chamberlain coordinate Question #2: Using the Chamberlain coordinate system, calculate a student’s displacement if they walk system, calculate a student’s displacement if they walk from Chamberlain to Bruner’s. from Chamberlain to Bruner’s.

How does your answer to question #2 compare to How does your answer to question #2 compare to question #1?question #1?

Question #3: Repeat the student displacement Question #3: Repeat the student displacement example, but use a coordinate system attached to the example, but use a coordinate system attached to the student!! Compare your result to the result for student!! Compare your result to the result for Question #2.Question #2.

Basic Concepts Of MechanicsBasic Concepts Of MechanicsA student leaves the TSU science building and walks A student leaves the TSU science building and walks to Bruner’s then to Chamberlain and finally returns to Bruner’s then to Chamberlain and finally returns back to the Science building. Answer the following two back to the Science building. Answer the following two questions for the student’s complete trip using the TSU questions for the student’s complete trip using the TSU coordinate system:coordinate system:

Question 4: What is the distance walked by the Question 4: What is the distance walked by the student?student?

Question 5: What is the student’s displacement?Question 5: What is the student’s displacement?