+ Chapter 7: Sampling Distributions Section 7.3 Sample Means.
Physics chapter 7.3 and 8
-
Upload
shaffelder -
Category
Technology
-
view
329 -
download
1
description
Transcript of Physics chapter 7.3 and 8
![Page 1: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/1.jpg)
Chapter 7.3 and 8
Circular and Planetary Motion
![Page 2: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/2.jpg)
Rotational Inertia The resistance of an object to changes in its
rotational motion. Question: Which way is easier to balance? Question: Which easier to rotate? Rotational Inertia increases as you move the
mass away from the axis of rotation Example is a Baseball bat. Long Bat held near
the end has more rotational motion than one that is “choked up” Players are told to choke up in order to get the speed of the bat going.
![Page 3: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/3.jpg)
Rotational Inertia An ice skater can spin around really fast by decreasing
their rotational axis. How do they do it? By pulling their arms in and thus increasing their
rotational speed. Here is our example: One of you will do this. This is exactly how you do flips in gymnastics and
cheerleading. Question: Why is the rotational inertia greater for a
gymnast when she’s swinging at full length or executing a somersault?
Question: Why do you hold your arms out to balance on a tight rope?
Question: Which can will roll down the incline faster? Beans or Juice?
![Page 4: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/4.jpg)
Speed and Acceleration in a Circle
You can find the speed in a circle by the following formula.
V = 2πr / T
![Page 5: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/5.jpg)
Centripetal Notes Centripetal means center seeking Centripetal acceleration – acceleration
towards the center of circleac = v2 / r
ac = 4π2r / T2
Centripetal Force – Force that is directed towards the center; it allows an object to follow a circular path
Fc = m ac
![Page 6: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/6.jpg)
Scientists
Tycho Brahe – believed in an earth centered universe
Johannes Kepler – believed in a sun centered universe
![Page 7: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/7.jpg)
Kepler’s Laws of Planetary Motion
1. The paths of the planets are ellipses with the center of the sun at one focus.
2. An imaginary line from the sun sweeps out equal areas in equal time intervals. Thus, the planets move fastest when closest to the sun.
3. Ratio of the squares of the periods of any two planets revolving about the sun is equal to the ratio of the cubes of their average distance from the sun.
![Page 8: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/8.jpg)
Formula for Kepler’s Laws
T2
T1
=
2
r1
r2
3
![Page 9: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/9.jpg)
Newton’s Universal Law of Gravitation
States that the attractive force between two objects is directly proportional to the product of the masses and inversely proportional to the square of the distance between the objects centers.
![Page 10: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/10.jpg)
Law of Gravitation
F = G (m1) (m2) / d2
F = Force in NewtonsG = Gravitational ConstantM = mass in kgD = distance in meters
![Page 11: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/11.jpg)
Henry Cavendish found the value of G
G = 6.67 x 10 -11 Nm2/kg2
![Page 12: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/12.jpg)
Satellite Motion
How do satellites stay in orbit? By the amount of speed, satellites
are always falling. They have enough speed to outrun
the curvature of the earth. V2 = GMo/ro
![Page 13: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/13.jpg)
Newton’s Variation of Kepler’s Third Law
T2 = 4 π2 ro3 / G Mo
Orbital radius for a satellite is:
ro = rp + h
![Page 14: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/14.jpg)
Newton’s Variation of Kepler’s Third Law (Derivation)
m v2 / r = G m M / r2 & v = 2 π r / T
v2 / r = G M / r2 canceling m
4 π2 r2 / T2 r = G M / r2 plug in for v
G M T2 r = 4 π2 r4 cross multiply
T2 = 4 π2 r3 / G M solve for T
![Page 15: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/15.jpg)
Satellite orbits
http://science.nasa.gov/Realtime/jtrack/3d/JTrack3D.html
![Page 16: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/16.jpg)
Gravitational Fields
Michael Faraday came up with the concept that a “field” is required for a magnet to attract an object.
This concept was later applied to the “gravitational fields”. Anything with mass has a gravitational field
![Page 17: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/17.jpg)
Gravitational Fields
g = F / m
g = N/kg (units)
Use these units for gravity not near the
surface of a planet (gravitational field)
![Page 18: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/18.jpg)
Determining the gravity of a planet
mg = G m Mp / rp2
g = G Mp / rp2
What is the gravity on your planet? How much does a 980N adult
weigh on your planet?
![Page 19: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/19.jpg)
Weightlessness
Caused when an object is in freefall
![Page 20: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/20.jpg)
Other Gravity Scientist
Galileo Galilei - Discovered gravity makes things fall at the same rate if not affected by air resistance
![Page 21: Physics chapter 7.3 and 8](https://reader036.fdocuments.in/reader036/viewer/2022062707/557e2207d8b42a08748b54de/html5/thumbnails/21.jpg)
Other Gravity Scientist
Albert Einstein - Developed theories of general and special relativity and showed that mass curves space. Black holes are so massive that light will not escape the space they curve.