Ch5marellal

toc Chapter 5 Circular Motion = The Physics Classroom: Characteristics of Circular Motion- Lesson 1=

a) Speed and Velocity
 * -Calculating Average Speed**

b) Acceleration
 * -Calculating Average Acceleration**

c) The Centripetal Force Requirement -an inward force must be acting upon it in order to cause its inward acceleration
 * -It is required! That...**

d) The Forbidden F-Word?!?!?! -Pilots at an air show perform a loop-the-loop. The pilots are oriented upside down at the top of the loop. They do not fall out due to inertia and centripetal force. Their natural tendency is to continue tangent to the curved path, but the gravitational force (and perhaps some normal force) pushes them center-ward. This centripetal force allows for circular motion.
 * -Pilots are saved!**

e) Mathematics of Circular Motion
 * -Calculating Circular Motion**

= The Physics Classroom: The Clockwork Universe- Lesson 2 =

a) Newton's Second Law (revisited) - -Forces pointing to the center of the circle are postive -Make an FBD, state the given info, find vertical and horizontal components if needed, use circular motion equations (Newton's 2nd law) to find any other possible info, use to solve for question asked

b) Amusement Park Physics  -Loops (vertical circle rules apply)  -Small hills and dips (vertical circle rules)  -Banked turns (normal and frictions forces break into two components)

c) Athletics  -Make an FBD, state given info, make vertical and horizontal components, use circular motion equations to solve for everything else, solve asked question  -Turning motions  -Solve these problems like a banked turn problem = =

= The Physics Classroom: Universal Gravitation- Lesson 3=

a) Gravity is More Than a Name -Not to be confused with the force of gravity ( **Fgrav** ), the acceleration of gravity ( **g** ) is the acceleration experienced by an object when the only force acting upon it is the force of gravity. -On and near Earth's surface, the value for the acceleration of gravity is approximately 9.8 m/s/s.

b) The Apple, The Moon, and The Inverse Square Law -Kepler's Three Laws of Planetary Motion -Force of gravity between Earth and any other object can be expressed through Fg = 1/d^2
 * The paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)
 * An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)
 * The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)

c) Newton's Law of Universal Gravitation -Fg = m1xm2/d^2, force of gravity is equal to mass 1 times mass 2 divided by distance between the two centers squared -G = 6.67 x 10-11 N m2/kg2

d) Cavendish and the Value of G -proved the value of G through his mercury, lead, mass experiment (see notebook for drawing)

e) The Value of g - Fg=mg (w) -

= The Physics Classroom: Planetary and Satellite Motion- Lesson 4=

a) Kepler's Three Laws -(look above for official Kepler's laws, "The Apple, the Moon, and the Inverse Square Law") -1st law: all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse -2nd law: a planet moves fastest when it is closest to the sun and slowest when it is furthest from the sun. Yet, if an imaginary line were drawn from the center of the planet to the center of the sun, that line would sweep out the same area in equal periods of time -3rd law: the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets: T2/R3 - T2/R3 can be applied as a ratio to any man-made satellite put around the Earth

b) Circular Motion Principles for Satellites -Satellite: any object orbiting the Earth, sun, or other massive body (moon, planets, comets) -Orbiting satellite requires a centripetal force -In elliptical satellite orbits, acceleration and net force vectors point towards center body

c) Mathematics of Satellite Motion -velocity: -acceleration: -final equation, Newton's form of Kepler's third law: ^T= period, R= average radius of orbit (distance from center of central planet, and G=6.67 x 10-11

d) Weightlessness in Orbit - Weightlessness is simply a sensation experienced by an individual when there are no external objects touching one's body and exerting a push or pull upon it. -A scale reading is actuallya measure of the upward force applied by the scale to balance the downward force of gravity acting upon an object -Force of gravity = mass x gravity

e) Energy Relationships for Satellites - - -