1. 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

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

3. Purdue University, Physics 220
Centrifuge
22,000 rpm
Rotor ,336 x g
Rotor ,228 x g
Lecture 8
Purdue University, Physics 220

4. 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

5. 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

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

7. 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

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. Purdue University, Physics 220
Orbits of Planets
Tycho Brahe ( )
Johannes Kepler ( )
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

12. 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

13. 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

14. 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

15. 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

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

17. 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

18. 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

19. 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

20. 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

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