Purdue University, Physics 220 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

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

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

Purdue University, Physics 220 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

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

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

Purdue University, Physics 220 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 First run at 4 second period, then do the PIQ. Then run at 2 second period. Stop it and show the forces. Acceleration is in the direction of the net force, which must be toward the center of the circle of motion. Lecture 8 Purdue University, Physics 220

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

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

Circular Orbits of Planets Lecture 8 Purdue University, Physics 220

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

Purdue University, Physics 220 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

Purdue University, Physics 220 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

Purdue University, Physics 220 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

Purdue University, Physics 220 Kepler’s Laws Elliptical orbits… Equal areas in equal time T2 = R3 These were empirical laws Lecture 8 Purdue University, Physics 220

Newton’s Law of Universal Gravitation From Kepler's 3rd Law, Newton deduced inverse square law of attraction. G=6.67 ´ 10-11 N m2/kg2 Your book derives Kepler’s third law from Newton’s law for a circular orbit Lecture 8 Purdue University, Physics 220

Purdue University, Physics 220 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

Purdue University, Physics 220 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 a = v2/r and a goes as 1/r so v goes as 1/sqrt(r). Lecture 8 Purdue University, Physics 220

Purdue University, Physics 220 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 Green has the greater centripetal force so from second law it has the greater acceleration. If they have trouble with this, remind them to draw a FBD and give them F = GMm/r2 Lecture 8 Purdue University, Physics 220

Purdue University, Physics 220 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

Purdue University, Physics 220 Artificial Gravity Lecture 8 Purdue University, Physics 220