Galileo and Inertia

1. Galileo and Inertia In the early 1600's, the Italian Physicist Galileo Galilee perfected the concept of modern experimental physics and made one of the most important discoveries in history. In his experiments, Galileo studied the motion of objects by rolling balls down wooden inclined planes.

2. Galileo and Inertia Since Galileo knew about friction, he sanded his inclined planes and used water and other lubricants (oils) to reduce the friction. As the friction was reduced, the ball rolled farther. Galileo then did something ingenious. He allowed the ball to roll up a second plane!!

3. Galileo and Inertia

4. Galileo and Inertia Regardless of the angle of inclination of the second inclined plane or its distance from the first inclined plane, the ball always appeared to roll up the second inclined plane until the ball reached its original height. If the inclined plane was not as steep, the ball would simply roll a greater distance. It was as if the ball somehow remember its starting height!! This discovery was contradictory to Aristotelian Mechanics!!

5. Galileo and Inertia Galileo then asked himself a brilliant question!! If the inclined plane had an angle of inclination of zero (i.e. it was horizontal), when would the ball reach its original height?

6. Galileo and Inertia Answer: It would never reach its original height so it would never stop!! Galileo therefore concluded that the “natural” state of motion is not rest!!

7. Galileo and Inertia Galileo knew that the Earth was a sphere and the ball appeared to keep rolling along the surface of the sphere. He also believed that the planets including the Earth traveled in circular orbits at constant speeds (uniform circular motion) around the sun. Thus, Galileo decided that all objects continue in uniform circular motion unless a net push or pull (i.e. force is applied) to the object.

8. Galileo and Inertia Thus, Galileo was able to explain why objects don’t fall off the Earth as it spins on its axis or rotates around the sun. Although Galileo experiments were brilliant, he was incorrect about the natural state of motion since he didn’t know about the concept of gravity. Rene Descart refined Galileo’s work by stating that the natural state of motion of an object is a straight line at constant speed and not a curved path. The concept of inertia was given its final form by the great Sir Isaac Newton as Newton’s 1st Law.

9. Newton’s 1st Law of Mechanics A particle will continue is a straight line at constant speed unless acted upon by a net push or pull (i.e. force). The property of a body to continue in a straight line at constant speed is called Inertia. Mass is the measure of a body’s inertia. Thus, a 2 kilo- gram object has twice the inertia of a 1 kilo-gram object.

10. Newton’s 1st Law of Mechanics Newton’s 1st Law tells us a couple of things: The natural state of mater is a straight line at constant speed. If an object is not moving in a straight line and/or if it is speeding up or slowing down then a net push or pull must be acting upon the body.

11. Newton’s 1st Law Question 1: Since an apple speeds up as it falls to the ground, what does Newton’s 1st Law say about the net push or pull on the apple? Question 2: When an object is dropped from a very high place, the object will initially pickup speed until it reaches some maximum speed (terminal speed) after which its speed stays constant. What does Newton’s 1st Law say about the net push or pull on the object once it reaches terminal speed?

12. Newton’s 1st Law Question 3: Why does a spaceship need an engine to blast off from the Earth or land on the moon, but not during the trip from the Earth to the Moon?

13. Basic Concepts Of Mechanics Question: How do we describe the location of an object? Answer: We specify its location in terms of an agreed upon set of directions and by measuring the distance from the object to some reference (possibly a tree). East McDonald’s South TSU Science Building

14. Basic Concepts Of Mechanics Scientist say that you are specifying your coordinate axis (i.e. the set of agreed upon directions and your origin). In this example, we might designate the directions x and y as well our reference point (origin) as the TSU science building. y McDonald’s x TSU Science Building

15. Basic Concepts Of Mechanics The arrow showing us the location of McDonald’s is called McDonald’s position vector. A vector is a mathematical quantity that has both (size) magnitude and direction! You must not only tell the visitor how far it is to McDonald’s, but also the direction to walk. y McDonald’s 600 m 20° x TSU Science Building

16. Basic Concepts Of Mechanics Sonic The mathematics of vectors is very different from the math of scalars (i.e. regular numbers) which you are accustomed to using!! It is not 900 m to Sonic from the Science Building nor do you walk towards McDonald’s!! 300 m y McDonald’s 600 m 20° x TSU Science Building

17. Basic Concepts Of Mechanics Vectors can be added by drawing the vectors to scale using a ruler and a protractor. This is how explorers Like Columbus charted their course and is still used by the Navy today!! Example: Add the following two vectors using the scale 1 cm = 1 m. 12 m 10 m 120° 30°

18. Basic Concepts Of Mechanics y To simplify the math, we will restrict ourselves in this course to 1-dimensional problems. Thus, we can specify the direction of our vectors by the sign of our answer. For example, the location of Bruner’s is +3000 m and the location of Chamberlain is -1500 m. 3000 m 1500 m x TSU Science Building Chamberlain School Bruner’s

19. Basic Concepts Of Mechanics y Question: What would be the position vectors for the following three locations (Chamberlain, Science building, and Bruner’s) using a coordinate system whose origin was at Chamberlain? 3000 m 1500 m x TSU Science Building Chamberlain School Bruner’s

20. Basic Concepts Of Mechanics Note: The position of an object is not unique!! It always depends on your coordinate system. In every problem, you must first specify your coordinate system and then determine the position vector for an object!

21. Basic Concepts Of Mechanics Displacement: The displacement of an object is defined as the change in the object’s position vector. Displacement = (Final Position) – (Initial Position) Question #1: Using the TSU science building coordinate system, calculate a student’s displacement if they walk from Chamberlain to Bruner’s.

22. Basic Concepts Of Mechanics Question #2: Using the Chamberlain coordinate system, calculate a student’s displacement if they walk from Chamberlain to Bruner’s. How does your answer to question #2 compare to question #1? Question #3: Repeat the student displacement example, but use a coordinate system attached to the student!! Compare your result to the result for Question #2.

23. Basic Concepts Of Mechanics A student leaves the TSU science building and walks to Bruner’s then to Chamberlain and finally returns back to the Science building. Answer the following two questions for the student’s complete trip using the TSU coordinate system: Question 4: What is the distance walked by the student? Question 5: What is the student’s displacement?