Chapter 7 Circular Motion Newton’s Laws of Universal Gravitation Motion in Space

 circular motion – when any object revolves about a single point (axis of rotation)  tangential speed – the speed of an object in circular motion  tangential speed (v t ) depends on the distance of the object from the axis of rotation  centripetal acceleration – the acceleration directed toward the center of a circular path (the word “centripetal” means “center seeking”)  a c = v t 2 /r (r = radius of the circular path)  centripetal acceleration is due to change in direction  tangential acceleration (a t ) is due to change in speed  centripetal force – the net force of an object in uniform circular motion  F c = mv t 2 /r (from F c = ma c )  inertia is overcome by the centripetal force Circular Motion Notes

Let’s try together: Page 235 Sample Problem A Page 237 Sample Problem B Try on your own: Page 236 Practice A #2-4 Page 238 Practice B #1&2

~ one partner read pages 240 & 241 ~ one partner read pages 244 & 245 ~ one partner read pages 246 & 247 ~ each partner write down 3 important facts ~ share and explain facts with each other

AGENDA: 1)Review universal gravitation math 2)Review universal gravitation concepts 3)History of planetary motion STUDY: 1)Circular motion notes 2)Circular motion math problems 3)Universal gravitation notes 4)Universal gravitation problems 5)Planetary motion notes * Equations will be given

 gravitational force – the mutual force of attraction between particles of matter  F g = Gm 1 m 2 r 2  the gravitational force and the mass of an object are directly proportional  the gravitational force and the distance between the masses are indirectly proportional  a gravitational force exists between ALL objects and attracts objects to one another  high and low tides partly result from the difference between the gravitational force at Earth’s surface & at its center Newton’s Law of Universal Gravitation Notes

A brief history lesson… In ancient times, people (including Plato and Aristotle) believed that Earth was at the center of the universe and the sun and other planets orbited Earth in perfect circles. In the second century, Claudius Ptolemy theorized that planets travel in small circles while simultaneously orbiting Earth. In 1543, Nicolaus Copernicus proposed that Earth and other planets orbit the sun in perfect circles. A few years after Copernicus (and a generation before Newton’s law of universal gravitation), Johannes Kepler analyzed planetary motion and developed three laws of motion in space.

1)Each planet travels in an elliptical orbit around the sun. 2)An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals. Thus, planets travel faster when they are closer to the sun. 3) The square of a planet’s orbital period (T 2 ) is proportional to the cube of the average distance (r 3 ) between the planet and the sun. In other words, the time it takes for an object (ie: the moon) to revolve around another object (ie: Earth) is proportional to the distance between the two objects. Kepler’s Laws of Motion in Space

BLACK HOLES!

A.Pair up with a group that researched a different topic. B.Read paper aloud while other group follows along. C.Answer the follow questions: 1.Is the formatting correct (refer to the rubric and the APA document on 2.Is there an introduction, 3-5 body paragraphs, and a conclusion? 3.Do the introduction and conclusion paragraphs include the main ideas? 4.Is the grammar correct (remember: no “I”, “you”, etc.)? 5.Does the content make sense? 6.Does anything sound too much like a website)? 7.Are there 5 references with 3.edu and/or.gov? D. Switch roles. E. Make changes.