1. Lecture 8Purdue University, Physics 2201 Lecture 08 Circular Motion PHYSICS 220

2. Lecture 8Purdue University, Physics 2202 Unimportable: #8279AE55,6.00,6.00 #834C955A,6.00,6.00 #841D4BD2,2.00,2.00

3. Examination 1 Date: February 21, 2011 (no lecture on Feb 20 Time: 6:30-7:30 pm Place: Stewart 183 You may bring a crib sheet, handwritten, on 8.5 x 11 inch paper (you may write on both sides) Material covered: Chapters 1-5 of textbook Bring your student ID Adaptive learners must notify Prof. Pushkar that you want to use an alternative testing location There will be 12 multiple choice questions Lecture 8Purdue University, Physics 2203

4. Centrifuge Lecture 8Purdue University, Physics 220

5. Centrifuge Lecture 8Purdue University, Physics 220 22,000 rpm Rotor 1 - 24,336 x g Rotor 2 - 50,228 x g

6. Lecture 8Purdue University, Physics 2206 The centrifuge works using the sedimentation principle, where the centripetal acceleration causes more dense substances to separate out along the radial direction (the bottom of the tube). A centrifuge is a device used in many laboratories It can be used to separate particles or molecules –Or remove them The effective force causes the particle to move to the bottom of the test tube –Similar to artificial gravity

7. Lecture 8Purdue University, Physics 2207 A cell in a centrifuge

8. Lecture 8Purdue University, Physics 2208 iClicker What is the direction of the acceleration? A) Along the tension in the cable B) In a horizontal direction away from the center C) In a horizontal direction toward the center

9. Lecture 8Purdue University, Physics 2209 Ancient Greeks: The Geocentric Model implies Earth-Centered Universe Circular Orbits of Planets

10. Lecture 8Purdue University, Physics 22010 Circular Orbits of Planets Copernicus (1500's) Developed a mathematical model for a Sun-centered solar system –Published in De Revolutionibus –Dedicated the book to Paul III –The De Revolutionibus was placed on the Index of Prohibited Books in 1616 as a result of the Galileo affairGalileo affair –It was taken off the Index in 1758

11. Lecture 8Purdue University, Physics 22011 Circular Orbits of Planets

12. Lecture 8Purdue University, Physics 22012 Orbits of Planets Tycho Brahe (1546-1601) Made precise measurements of the positions of the planets Described the shape of planetary orbits as well as their orbital speeds Johannes Kepler (1571-1630)

13. Lecture 8Purdue University, Physics 22013

14. Lecture 8Purdue University, Physics 22014 Log a c versus log R a c  1/R 2

15. Lecture 8Purdue University, Physics 22015 Kepler’s Laws First law: The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

16. Lecture 8Purdue University, Physics 22016 Kepler’s Laws Second law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

17. Lecture 8Purdue University, Physics 22017 Kepler’s Third Law The square of a planet's orbital period is proportional to the cube of the length of its orbit's semimajor axis.

18. Lecture 8Purdue University, Physics 22018 Elliptical orbits… Equal areas in equal time T 2 ~ R 3 These were empirical laws Kepler’s Laws

19. Lecture 8Purdue University, Physics 22019 Newton’s Law of Universal Gravitation From Kepler's 3rd Law, Newton deduced inverse square law of attraction. G=6.67  10 -11 N m 2 /kg 2 Your book derives Kepler’s third law from Newton’s law for a circular orbit

20. Lecture 8Purdue University, Physics 22020 Satellites - Speed is independent of mass of satellite - Satellites in lower orbits have greater speeds Geostationary orbits: A circular orbit in Earth’s equatorial plane whose period is equal to Earth’s rotational period. ~35,786 km above ground

21. Lecture 8Purdue University, Physics 22021 iClicker Two identical (except for color) satellites are in circular orbits around the Earth. The red satellite is farther from the earth than the green one. Which satellite has the greater velocity? A) Red B) Green C) They are the same

22. Lecture 8Purdue University, Physics 22022 Exercise Two identical (except for color) satellites are in circular orbits around the Earth. The red satellite is farther from the earth than the green one. Which satellite has the greater centripetal acceleration? A) Red B) Green C) They are the same