Abdul Sameer Aggarwal Harshwardhan Ansari Nasar Aisha Case
• Abdul, Sameer • Aggarwal, Harshwardhan • Ansari, Nasar, Aisha • Case, Ryan, Patrick • Ducey, Alexander, Thomas • Goswami, Nimish • Hauser, Christa, Ann • Li, Jing • Lute, Aaron, M • Reisen, David, Paul • Shen, Yi • Thompson, Zachary, James • Woods, Arshiuna, Evette Lecture 8 Purdue University, Physics 220 1
PHYSICS 220 Lecture 08 Circular Motion Lecture 8 Purdue University, Physics 220 2
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). Lecture 8 Purdue University, Physics 220 4
Circular Motion – Centrifuge • 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
A cell in a centrifuge Lecture 8 Purdue University, Physics 220 6
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 7
Circular Orbits of Planets Ancient Greeks: The Geocentric Model implies Earth-Centered Universe Lecture 8 Purdue University, Physics 220 8
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 9
Circular Orbits of Planets Lecture 8 Purdue University, Physics 220 10
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 11
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 12
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 13
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 14
Kepler’s Laws Elliptical orbits… Equal areas in equal time T 2 = R 3 • These were empirical laws Lecture 8 Purdue University, Physics 220 15
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 16
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 17
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 18
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 19
Weightlessness • Inside the Space Shuttle, the astronauts experience apparent weightlessness. • The force of gravity on the Earth pulls on the astronauts to keep them in a circular orbit around the Earth, so we can’t accurately say there is “no gravity” there. • Both the astronauts and the Space Shuttle are in uniform circular motion, and are continually accelerating towards the Earth. The are both “falling” at the same rate. • The apparent weight (how heavy you feel) is defined as the magnitude of the normal force acting on the body: where g is the local gravitational field strength: Lecture 8 Purdue University, Physics 220 20
Artificial Gravity Lecture 8 Purdue University, Physics 220 21
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