1. Physics Part 1 MECHANICS
Draft (part C incomplete)
Topic II. Motion in one Dimension (Kinematics)
W. Pezzaglia
Updated: 2012Aug23

2. 2
II. Motion in 1D
Principle of Inertia
Uniform Motion
Acceleration

3. A. Principle of Inertia Aristotle’s Physics Inertia Motion is Relative3
A. Principle of Inertia
Aristotle’s Physics
Inertia
Motion is Relative

4. 1. Aristotle’s Physics 4 Natural state is rest
continuation of motion depends on continued action of a force [e.g. the “prime mover” (god) must continue to push the moon]
Antiperistasis: To explain how a ball rolls when no-one is pushing it: as ball rolls, it leaves empty space behind it. Nature abhors a vacuum, so air rushes in to fill the space vacated by the ball, hence continues to push the ball along, but it will eventually stop.
Aristotle: 384 BC-322 BC

5. 2. Inertia 5 (a) Impetus Theory:
Jean Buridan proposes motion continues because the mover has imparted some “impetus” to the object (which dissipates)
Suggests planets have “circular impetus”, continuing their orbits forever as there is no resistance in the heavens.
Jean Buridan

6. b. Natural Motion is Straight6
Giambattista Benedetti
Natural motion is straight, not circular
When projectile released from a sling, it goes straight.
His work influences Galileo
If string breaks, ball goes straight

7. c. Galileo’s Law of Inertia7
c. Galileo’s Law of Inertia
Bodies at rest tend to stay at rest
Bodies in uniform motion will tend to stay in uniform motion
Unless acted upon by an outside force
“natural state” IS motion
Galileo Galilei
Demo: Play 11:35-14:25 of MU #4:

8. 3. Motion is Relative 8 (a) Absolute Motion
Aristotle (350 BC) thought that the earth is at rest, the stars, sun and planets revolve around us
Aristarchus (250 BC) proposed that since the sun was bigger, that the earth goes around the sun.
Followers of Aristotle (e.g. Hipparchus 150 BC) argued that the earth cannot be moving, else falling bodies would fall sideways.
Hence, the earth must be at absolute rest.
Geocentric Theory
of the universe

9. 3b. The Earth Moves 9
Copernicus (1543 AD) shows that the complex motion of the planets can be more simply explained if the sun is at rest, and the earth revolves around it (“heliocentric theory”).
However, he doesn’t really address the issue of why falling bodies don’t fall sideways if the earth is moving.
Geocentric Theory
of the universe

10. 3c. Galileo: no absolute motion10
Galileo: (1632) Motion is relative. A ball dropped from the crow’s nest will hit at the base of the ship’s mast, even if the ship is moving. Hence, there is no absolute measure of motion (or rest).
Demo: Play 11:35-20:32 of MU #4:

11. 11
B. Motion
Motion in Time
Average Velocity
Instantaneous Velocity

12. 1. Motion in Time 12
What IS time? Time is what happens when nothing else does.
Why does time only flow forward?
Are all measurements of time indirect? (i.e. involve motion)

13. a. Descarte’s Graph 13 Cogito ergo sum (I think, therefore I am)
1637 Cartesian Coordinates
Geometry could be represented by algebraic equations
Hence path of motion (e.g. orbit of moon) could be described by an equation and plotted on a graph.
Rene Descartes

14. b. Motion in Time 14
Galileo is the first (I think) to represent motion by a graph of position with respect to time
An Event is a point in spacetime (x,t), saying the object is at position “x” at time “t”
Worldline of an object is a sequence of events

15. c. Velocity 15 Slope of worldline is velocity SI Units: meters/second
Equation of uniform motion (initial position x0 at time zero)

16. 2. Average Velocity Average Speed 16 Total distance 120 m
Total time: 15 seconds
Avg Speed=120/15= 8 m/s
What is the average speed here?

17. b. Displacement Displacement is the change in position 17 0 to 5 s
x=+60 m
x=-60 m
x=+0 m
Note “minus” displacement means movement backwards!

18. c. (Average) Velocity Velocity is speed with a direction 18 0 to 5 s
Time Interval
0 to 5 s
0 to 10 s
10 to 15 s
0 to 15 s
Average Velocity
v= 12 m/s
v= 6 m/s
v= -12 m/s
v= 0 m/s
The average velocity is zero because you end up where you started (but the average speed is NOT zero)

19. 3. Instantaneous Velocity19
(a) Tangent Line
Generally velocity changes with time.
Instantaneous velocity at a point is the slope of the tangent line

20. b. Secant Line 20
Its impossible to measure instantaneous velocity. Finite time t must pass.
Slope of secant line approximates instantaneous velocity if t is small.

21. c. The Derivative 21
Instantaneous velocity is actually the “derivative”.
Finding exact equations for tangent lines was the beginning of calculus
Example: Parabola 

22. C. Acceleration Falling Motion Uniform Acceleration22
C. Acceleration
Falling Motion
Uniform Acceleration
Kinematic Equations

23. 3. Acceleration Definition 23
Acceleration is the rate of change of velocity (i.e. change in velocity with respect to a change in time)
In first 30 seconds the velocity has gone from zero to 10 m/s. What is the acceleration?
What is the acceleration from 30 to 45 sec?
Zero! (no change in velocity)

24. 1. Falling Motion Aristotle’s Theory Galileo’s Law of Falling Bodies24
Aristotle’s Theory
Galileo’s Law of Falling Bodies
Einstein’s theory of gravity

25. Heavier balls will fall faster They fall at the same rate!
Law of Falling: Introduction 25
Aristotle:
Heavier balls will fall faster
Galileo:
They fall at the same rate!

26. (a) Aristotle and Falling Motion26
the rate of falling is proportional to the weight and inversely proportional to the density of the medium
the peripatetics (followers of Aristotle) postulated that the speed was proportional to the distance fallen.
Galileo shows that this must be wrong, for an object starting at zero speed would never acquire any speed!
Aristotle: 384 BC-322 BC

27. (b) Galileo’s Experiment at Pisa27
1590 Galileo’s Principle: all bodies fall at the same rate, regardless of mass
1907 Strong EEP (Einstein Equivalence Principle) same result, but Einstein argued from a different way.
Einstein proposed that falling bodies in gravity are equivalent to being in an accelerated frame (e.g. in an accelerating elevator)

28. (c) The Einstein Equivalence Principle28
Reference at rest with Gravity is indistinguishable to a reference frame which is accelerating upward in gravity free environment.
The apple accelerating downward due to gravity looks the same as an apple at rest in space, with the floor accelerating upward towards it.

29. 2. Uniform Acceleration Galileo’s Inclined Plane The law of squares29
Galileo’s Inclined Plane
The law of squares
Acceleration and velocity

30. 2a. Inclined Plane Experiments30
Falling motion is too fast to measure
Galileo shows rolling balls down inclined plane is same type of motion, but easier to measure because slower
Discovers falling motion has constant acceleration

31. 2b Galileo’s Law of Squares31

32. 2c. Results 32
Total distance “d” traveled is proportional to square of time
Equation:
Where “a” is the acceleration For gravity, a=g= 9.8 m/s2

33. 3. Kinematic Equations Velocity and Instantaneous Acceleration33
Velocity and Instantaneous Acceleration
Distance and (uniform) acceleration
The third kinematic equation

34. 3. Kinematic Equations 34
For constant acceleration (falling motion, or ball rolling down inclined plane):
Velocity increases linearly with time:
Distance increases with square of time:
Hence distance is related to velocity:

35. References
Descartes, R. La Géométrie. Livre Premier: Des problèmes qu'on peut construire sans y employer que des cercles et des lignes droites (Book one: Problems whose construction requires only circles and straight lines). (French)
Galileo, Two New Sciences (1638). Chapter “Third Day” discusses motion and acceleration.
Origin of terms abscissa and ordinate, see
SAT Physics:
Good Java Demo:

36. Video References
Inclined Plane short video:
Video: Mechanical Universe #2: Law of Falling bodies:
Video: Mechanical Universe #4: Inertia:
Galileo interview:
Galileo:
Video: Losey's 1975 adaptation of Brecht's play about Galileo Galilei
Part1, Invents (steals) the telescope
Part2, sells telescope to Venice, mountains on moon, moons of jupiter
Part3, The young duke refuses to look through telescope, first problem with church, Clavius says he's right
Part4, Meets cardinals Barberini and Bellarmine (that Copernicus is wrong)
Part5, Student priest has crises
Part6, needle floats, aristotle is wrong, sunspots, pope is dying
Part7, observe sunspots, play within play, more trouble with church
Part8, before inquisition, pope Barberini, recantation
Part9, under house arrest, smuggling out book Two New Sciences
Part10, ditribe on ethics of science