1. College Physics, 7th Edition
Lecture Outline
Chapter 7
College Physics, 7th Edition
Wilson / Buffa / Lou
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2. Chapter 7 Circular Motion and Gravitation
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3. FLT
Given a Circular motion of macroscopic objects, SWBAT to define, explain and calculate the centripetal acceleration and centripetal force
a= v2/r
Fc = mac = mv2/r
at certain condition such as :
a. critical conditions
b. equilibrium

4. Using mathematical representations of Newton’s Law of Gravitation and Kepler’s law , SWBAT  to describe the motion of a satellite and apply the concepts of angular momentum and torque.  
Using mathematical or computational representations , SWBAT to predict the motion of orbiting objects in the solar system .
Performance Expectations :
I can use mathematical representations of Newton’s Law of Gravitation to describe and predict the gravitational forces between two objects .
Learning Targets:
I can calculate the gravitational interaction between observable masses using Newton’s Law of Gravitation

5. Units of Chapter 7 Angular Measure Angular Speed and Velocity
Uniform Circular Motion and Centripetal Acceleration
Angular Acceleration
Newton’s Law of Gravitation
Kepler’s Laws and Earth Satellites
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6. 7.1 Angular Measure
The position of an object can be described using polar coordinates—r and θ—rather than x and y. The figure at left gives the conversion between the two descriptions.
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7. Example :
Given the cartesian/rectangular coordinates(5m, 10m) what are the polar coordinates?
Given the polar coordinates (2.5m, 53.13°) , what are the cartesian or rectangular coordinates?
#4 p 253 College Physics
Angles are expressed in degrees and radians .How do you convert degrees to radians and vice versa ?
Ex. 60°=_____radians(rad)
Π/2 = _____°
#2 p 253 College Physics

8. 7.1 Angular Measure
r is a distance that extends from the origin. r is the same for any point on a given circle. (like the radius!)
Θ is an angle, and it changes with time.
Linear Displacement…how do we calculate?
Angular Displacement is VERY similar

9. 7.1 Angular Measure Δθ = θ - θi
The unit for angular displacement is the degree.
There are 360 degrees in one complete circle.

10. 7.1 Angular Measure
The arc length, s, is the distance that is traveled along the circular path in meters
The θ is said to define the arc length.
It is most convenient to measure the angle θ in radians.

11. Sample Problems CW/HW :p 253
Classwork # 4, #2
Homework 5,6,7,8, p 253 College Physics

12. 7.1 Angular Measure
Relationship between arc length, the radius, and the angle:
For one full circle, with s = 2πr
(this is the circumference of the circle)
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13. 7.1 Angular Measure
A spectator standing at the center of a circular running track observes a runner start a practice race 256m due east of her own position. The runner runs on the track to the finish line, which is located due north of the observer’s position. What is the distance of the run?

14. 7.1 Angular Measure
A sailor sights a distance tanker ship and finds that it subtends an angle of 1.15 degrees. He knows from the shipping charts that the tanker is 150m in length. Approximately how far away is the tanker?

15. Sample Problems CW/HW :p 253 College Physics
Example #10
Class work #11

16. Sample Problems CW/HW :p 253

17. Design an Experiment Circular Motion
Purpose:
a. To measure the frequency (f) of a vertical circular motion for two different lengths .
b. To determine period (T) for two different lengths ,using T = 1/f
c. To calculate the angular velocity(ω) for two different lengths, using ω= 2Πf
d. To calculate the tangential velocity for two different lengths, (v) using
v = rω
e. To determine the centripetal acceleration (ac) ,for two different lengths using ac = v2 /r
f. To determine the centripetal Force (Fc) using Fc= mv2 / r
g. To calculate the tension of the string at the bottom and the top of the vertical circular motion .

18. 7.2 Angular Speed and Velocity
How do we calculate speed?
What’s the difference between average speed and instantaneous speed?

19. 7.2 Angular Speed and Velocity
In analogy to the linear case, we define the average and instantaneous angular speed:
Units??
Angular Velocity??
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20. 7.2 Angular Speed and Velocity
The direction of the angular velocity is along the axis of rotation, and is given by a right-hand rule.
How does this work?
Counterclockwise is positive
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21. 7.2 Angular Speed and Velocity
A particle moving in a circle has an instantaneous velocity tangential to its circular path.
What is a tangent?
Tangential speed (the particle’s orbital speed)

22. 7.2 Angular Speed and Velocity
Relationship between tangential and angular speeds:
This means that parts of a rotating object farther from the axis of rotation move faster.
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23. CW/HW Example : # 26p 254 Classwork : #27 – p 254 College Physics
26,27,28,29, 32
P 254 College Physics

24. 7.2 Angular Speed and Velocity
An amusement park merry go round at its constant operational speed makes one complete rotation in 45 seconds. Two children are on horses, one at 3.0 m from the center of the ride and the other farther out at 6.0 m from the center.
What are the angular speeds of each?
What are the tangential speeds of each?

25. Experiment : FREQUENCY FUN LAB

26. 7.2 Angular Speed and Velocity
The period is the time it takes for one complete revolution (rotation)
For example: The period of revolution of the Earth around the Sun is one year.
Or the period of the Earth’s axial rotation is 24 hours.
Units: seconds or sometimes seconds/cycle
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27. 7.2 Angular Speed and Velocity
the frequency is the number of revolutions (rotations) per second. [Units: Hertz]
The relation of the frequency to the angular speed:

28. 7.2 Angular Speed and Velocity
A CD rotates in a player at a constant speed of 200 rpm. What are the CD’s
Frequency?
Period?
CLASSWORK College Physics
# 27 / p 254

29. Centripetal Acceleration and Centripetal Force
P 226- X Centripetal Acceleration
P Y Centripetal Force
Write your information – 10 bullet information
Share your information

30. 7.3 Uniform Circular Motion and Centripetal Acceleration
What is uniform motion?
What is uniform circular motion?

31. 7.3 Uniform Circular Motion and Centripetal Acceleration
The acceleration in uniform circular motion is called centripetal acceleration.
Centripetal means “center-seeking.”
Centripetal acceleration is directed inward or “into” the circle.
The tangential velocity is perpendicular to the centripetal acceleration.

32. 7.3 Uniform Circular Motion and Centripetal Acceleration
Instantaneous centripetal acceleration
Can also be written as…
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33. 49, 50

34. 7.3 Uniform Circular Motion and Centripetal Acceleration
A laboratory centrifuge operates at a rotational speed of 12,000 rpm.
What is the magnitude of the centripetal acceleration of a red blood cell at a radial distance of 8.00 cm from the centrifuge’s axis of rotation?
How does this acceleration compare with g?

35. 7.3 Uniform Circular Motion and Centripetal Acceleration
The centripetal force (net inward force) is the mass multiplied by the centripetal acceleration.
This force is the net force on the object. As the force is always perpendicular to the velocity, it does no work.
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36. Design AN Experiment Flying Pig- Circular Motion
I. Purpose: Given a Flying Pig in circular Motion, determine the radius of the circular motion,its frequency, its period, its angular velocity , tangential velocity, centripetal acceleration ,Centripetal force and tension on the string II. Materials : Flying pig, meter stick, digital scale,stopwatch

37. DATA Table Radius,m T, sec f ,Hz W=2∏f Rad/s V=rw m/s Centripetal
Acceleration
Centripetal force

38. Design an Experiment Circular Motion
Purpose
a. To measure the frequency (f) of a vertical circular motion .
b. To determine period (T)
c. To calculate the angular velocity(ω) using ω= 2Πf
d. To calculate the tangential velocity (v) using
v = rω
e. To determine the centripetal acceleration (ac) using ac = v2 /r
f. To determine the centripetal Force (Fc) using Fc= mv2 / r
g. To calculate the tension of the string at the bottom and the top of the vertical circular motion .
h. To compare the tangential velocity v with 2 different radius r

39. Design an Experiment Circular Motion
Purpose
a. To measure the frequency (f) of a vertical circular motion .
b. To determine period (T)
c. To calculate the angular velocity(ω) using ω= 2Πf
d. To calculate the tangential velocity (v) using
v = rω
e. To determine the centripetal acceleration (ac) using ac = v2 /r
f. To determine the centripetal Force (Fc) using Fc= mv2 / r
g. To compare the tangential velocity for 2 different lengths
V vs r

40. 7.3 Uniform Circular Motion and Centripetal Acceleration
A ball is attached to a string is swung with uniform motion in a horizontal circle above a person’s head. If the string breaks, which of the trajectories shown on the following slide would the ball follow.

41. 7.4 Angular Acceleration
The average angular acceleration is the rate at which the angular speed changes:
In analogy to constant linear acceleration:
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42. 7.4 Angular Acceleration
If the angular speed is changing, the linear speed must be changing as well. The tangential acceleration is related to the angular acceleration:
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43. 7.4 Angular Acceleration
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44. CFA Circular Motion

45. 3. A merry go round makes 24 revolutions in a 3 minute ride
A. What is the angular speed in rad/s
B. What are the tangential speeds of two people 4m and 5m from the center or axis of rotation
4. Draw and label in a circular motion :
Radius, angular velocity, tangential velocity, centripetal force and centripetal acceleration, tangential acceleration and angular acceleration
5. The moon revolves around the earth in 27.3 days in a nearly circular orbit with a radius of 3.8 X 10(5) km. Assuming the moon’s moon orbital motion is uniform circular motion, what is the moon’s acceleration as it “falls” toward the earth ?

46. 7.5 Newton’s Law of Gravitation
Newton’s law of universal gravitation describes the force between any two point masses:
G is called the universal gravitational constant:
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47. CW : Universal Law of Gravitation
# 80 p 257- College Physics
#s p – Conceptual Physics

48. 7.5 Newton’s Law of Gravitation
Gravity provides the centripetal force that keeps planets, moons, and satellites in their orbits.
We can relate the universal gravitational force to the local acceleration of gravity:
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49. 7.5 Newton’s Law of Gravitation
The gravitational potential energy is given by the general expression:
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50. 7.6 Kepler’s Laws and Earth Satellites
Kepler’s laws were the result of his many years of observations. They were later found to be consequences of Newton’s laws.
Kepler’s first law:
Planets move in elliptical orbits, with the Sun at one of the focal points.
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51. 7.6 Kepler’s Laws and Earth Satellites
Kepler’s second law:
A line from the Sun to a planet sweeps out equal areas in equal lengths of time.
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52. 7.6 Kepler’s Laws and Earth Satellites
Kepler’s third law:
The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun; that is,
This can be derived from Newton’s law of gravitation, using a circular orbit.
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53. 7.6 Kepler’s Laws and Earth Satellites
If a projectile is given enough speed to just reach the top of the Earth’s gravitational well, its potential energy at the top will be zero. At the minimum, its kinetic energy will be zero there as well.
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54. 7.6 Kepler’s Laws and Earth Satellites
This minimum initial speed is called the escape speed.
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55. 7.6 Kepler’s Laws and Earth Satellites
Any satellite in orbit around the Earth has a speed given by
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56. 7.6 Kepler’s Laws and Earth Satellites
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57. 7.6 Kepler’s Laws and Earth Satellites
Astronauts in Earth orbit report the sensation of weightlessness. The gravitational force on them is not zero; what’s happening?
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58. 7.6 Kepler’s Laws and Earth Satellites
What’s missing is not the weight, but the normal force. We call this apparent weightlessness.
“Artificial” gravity could be produced in orbit by rotating the satellite; the centripetal force would mimic the effects of gravity.
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59. Summary of Chapter 7
Angles may be measured in radians; the angle is the arc length divided by the radius.
Angular kinematic equations for constant acceleration:
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60. Summary of Chapter 7
Tangential speed is proportional to angular speed.
Frequency is inversely proportional to period.
Angular speed:
Centripetal acceleration:
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61. Summary of Chapter 7 Centripetal force:
Angular acceleration is the rate at which the angular speed changes. It is related to the tangential acceleration.
Newton’s law of gravitation:
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62. Summary of Chapter 7 Gravitational potential energy: Kepler’s laws:
Planetary orbits are ellipses with Sun at one focus
Equal areas are swept out in equal times.
The square of the period is proportional to the cube of the radius.
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63. Summary of Chapter 7 Escape speed from Earth:
Energy of a satellite orbiting Earth:
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