PHYSICS 220 Lecture 08 Circular Motion Lecture 8

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

• Unimportable: • #8279 AE 55, 6. 00 • #834 C 955 A, 6. 00 • #841 D 4 BD 2, 2. 00 Lecture 8 Purdue University, Physics 220 2

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 8 Purdue University, Physics 220 3

Centrifuge Lecture 8 Purdue University, Physics 220

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

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 Lecture 8 Purdue University, Physics 220 6

A cell in a centrifuge Lecture 8 Purdue University, Physics 220 7

i. Clicker 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 Lecture 8 Purdue University, Physics 220 8

Circular Orbits of Planets Ancient Greeks: The Geocentric Model implies Earth-Centered Universe Lecture 8 Purdue University, Physics 220 9

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 affair – It was taken off the Index in 1758 Lecture 8 Purdue University, Physics 220 10

Circular Orbits of Planets Lecture 8 Purdue University, Physics 220 11

Orbits of Planets Tycho Brahe (1546 -1601) Johannes Kepler (1571 -1630) • Made precise measurements of the positions of the planets Lecture 8 • Described the shape of planetary orbits as well as their orbital speeds Purdue University, Physics 220 12

Lecture 8 Purdue University, Physics 220 13

Log ac versus log R ac 1/R 2 Lecture 8 Purdue University, Physics 220 14

Kepler’s Laws • First law: The orbit of a planet about the Sun is an ellipse with the Sun at one focus. Lecture 8 Purdue University, Physics 220 15

Kepler’s Laws • Second law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time. Lecture 8 Purdue University, Physics 220 16

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. Lecture 8 Purdue University, Physics 220 17

Kepler’s Laws Elliptical orbits… Equal areas in equal time T 2 ~ R 3 • These were empirical laws Lecture 8 Purdue University, Physics 220 18

Newton’s Law of Universal Gravitation • From Kepler's 3 rd 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 Lecture 8 Purdue University, Physics 220 19

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 Lecture 8 Purdue University, Physics 220 20

i. Clicker 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 Lecture 8 Purdue University, Physics 220 21

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 Lecture 8 Purdue University, Physics 220 22