1. Are you registered to vote in Colorado, or interested in getting registered? (Deadline is October 3 to register) The election this year is "off-cycle", but that doesn't mean you should ignore it. There are ballot issues this year that can (and will) directly impact you, and I encourage you to Get informed, and choose to vote! http://www.colorado.edu/physics/phys2010/phys2010_fa11/vote.html https://www.sos.state.co.us/Voter/secuRegVoterIntro.do

2. Announcements CAPA Set #6 due Friday at 10 pm CAPA Set #7 now available, due next Friday Next week in Section  Assignment 4: Circular Motion & Gravity Finish reading all sections of Chapter 5 Advanced reminder  Exam #2 on Tuesday, October 11 Reminder about office hours … Nagle (Monday 2-3 in office, Wednesday 1:45-3:45 pm help room) Kinney (Thursday 4-5 pm help room) Uzdensky (Tuesday 11am-noon help room) If you find a missing clicker, please bring it to me or the Main Physics Office

3. Circular Motion – fixed radius and at constant speed |v| Always accelerating due to change in direction of velocity vector. Centripetal acceleration inwards towards the circle center with magnitude |a| = v 2 /r

4. “Wall-of-Death” But don’t I feel out outward force? This is a “fictitious” force, not real.

5. Consider the “Wall-of-Death” Which diagram correctly shows the real forces on the rider? “Centripetal force”: a real force. Clicker Question Room Frequency BA Fictitious force: “centrifugal force” – in the rider’s frame. Centrifugal force (from Latin centrum, meaning "center", and fugere, meaning "to flee“)

6. 1 2 3 What are the three forces #1, 2, 3? A) 1 - gravity 2 - centrifugal force 3 – friction B)1 – friction 2 – normal force of the wall 3 – gravity C) 1 - centripetal force 2 – normal force of the wall 3 – friction D)1 – friction 2 – centrifugal force 3 - gravity Clicker Question Room Frequency BA

7. r m Choose a coordinate system: Usually radial and tangential. For uniform motion, velocity in the tangential direction is constant, so Σ F T = m a T = 0 In the radial direction: Σ F R =m a R = mv 2 /r Tangential (T) Radial (R) Dynamics of Uniform Circular Motion

8. For every case of uniform circular motion, there must be a force directed towards the center. We say there is a centripetal force. However, there is always a specific force that is acting. There is no “circle force”. Circular motion does not cause a force. Ball circling around tied to a string. Centripetal force  Tension Force Wall of Death ride Centripetal force  Normal Force Race Car driving in circle Centripetal force  Friction Force

9. Spinning Bucket of Water

10. The Earth circles the Sun at an average distance of 1 Astronomical Unit = 1.5 x 10 11 meters in one year. What is its orbital centripetal acceleration? r = 1 AU E Sometimes we quote accelerations relative to g (9.81 m/s 2 ).

11. The Earth circles the Sun at an average distance of 1 AU = 1.5 x 10 11 m in 1 year. What’s causing the centripetal acceleration? A)The electrostatic force between the Earth and Sun. B)The tension in the string connecting the Earth to the Sun. C)The force of gravity between the Earth and the Sun. D)Depends on the time of day. r = 1 AU E τ = 365 days Clicker Question Room Frequency BA

12. Newton’s Law of Universal Gravitation Insight: what keeps the Moon in orbit around the Earth and the Earth in orbit around the Sun is exactly the same thing that causes an “apple to fall from a tree”. “Every particle in the universe attracts every other particle.”

13. “Every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. The force points along the line joining the two particles.” Newton’s Law of Universal Gravitation

14. Universal Gravitation Verification 1687: Isaac Newton published Gravity Theory 1798: Henry Cavendish confirmed this formula experimentally 1915: Albert Einstein’s General Theory of Relativity explained why gravity behaves this way.

15. How Strong is Gravity? r = 1 meter m 1 = 70 kgm 2 = 70 kg That is about 1/60th the weight of a single hair.

16. Who does the force act on? r = 1 meter m 1 = 70 kgm 2 = 70 kg Answer = Both Person #1 exerts a force on Person #2 Person #2 exerts a force on Person #1

17. Objects are extended in space. Newton’s Law of Universal Gravitation is based on computing the distance between two objects, but which distance? R CM Extended Objects In fact, every part of object #1 exerts a gravitational attraction on every part of object #2, and vice versa. When adding all vector components, we treat the force as acting between the “center of mass” of each object. “Center of mass” for sphere = middle

18. Consider the force of gravity exerted by the Earth with mass M E on a person of mass m on its surface? RERE Big G, Little g Gravitational force on an object on the surface of the earth!

19. You are standing on the surface of the earth. The earth exerts a gravitational force on you F earth, and you exert a gravitational force on the earth F person. Which of the following is correct: A)F earth > F person B)F earth < F person C)F earth = F person D)It’s not so simple, we need more information. Clicker Question Room Frequency BA Newton’s Third Law