1. Circular Motion & Universal Gravitation
Chapter 7
Circular Motion
& Universal Gravitation

2. Rotation and Revolution
Rotation (spin) - spin about an axis located within the body. Ex: ballerina
Revolution - object turns about an external axis. Ex: moon around the earth

3. Uniform Circular Motion
Continues in a circle with the same tangential velocity
What keeps it going in a circle?
Any acceleration?

4. Uniform Circular Motion
Centripetal (center seeking)
vs. Centrifugal (towards outside)

5. Uniform Circular Motion
Hammer throw/sling
Space station
Water glass

6. Uniform Circular Motion
Centripetal acceleration depends on tangential velocity and radius
acent = vtangent2/r

7. Uniform Circular Motion
Centripetal Force
F = ma, so Fcent = acent*mass
Fcent = (mv2)/r
Force must come from something else, IT IS A NET FORCE!!!!!!
Can be tension (Ball on string), normal (washing machine), friction (ramp)

8. Uniform Circular Motion
Mini-lab
Finding the Force in the string

9. Coriolis Effect Hurricanes Warships Toilets?

10. Why do things fall? Greeks levity (smoke, helium balloons) vs.
gravity (rocks, apples)
Gave us the term, but not why

11. Understanding the Heavens
Ancients thought heavens very different from earth
Tycho Brahe devoted his life to taking careful measurements and records of the motion of planets, stars, and comets

12. Understanding the Heavens
Johannes Kepler became an assistant of Tycho
After Tycho died, Kepler used his extensive data to formulate 3 laws about planetary motion

13. Kepler’s Laws
The paths of the planets are ellipses with the center of the sun at 1 foci
A planet sweeps out equal area in equal time intervals

14. Kepler’s Laws

15. Kepler’s Laws
Soon after Kepler published his laws Galileo made detailed observations of Jupiter’s 4 largest moons through the first telescope
Io – 4.2 unit radius, 1.8 day period
Ganymede – 10.7 unit radius, ?? period

16. Universal Gravitation
Newton took Kepler’s ellipse idea and calculated the force on the planet must be proportional to 1/d2
Further reflection, (apple) led him to conclude F also depended on the masses involved

17. Universal Gravitation
F = G*m1*m2/d2
G is universal gravitational constant
This is an inverse square law, (butter gun)

18. Universal Gravitation
Newton’s Law of Universal Gravitation confirmed Kepler’s 3rd law
Newton didn’t know G and couldn’t find it from the planets since he didn’t know the mass of any of them

19. Cavendish’s Experiment
Weighing the Earth
Cavendish found G by using 2 known masses and arranging the experiment carefully so he could measure the (tiny) force
With G and the mass of any object on earth he could find the earth’s mass

20. Weighing the Earth F = G*m1*m2/d2
On the surface of the earth G, Me, and the radius don’t change Only the 2nd mass changes
G*Me/r2 = g
Ergo: Fg = mg

21. Orbiting objects Newton’s cannon
Objects orbit because gravity supplies a centripetal force
G*Mem/r2 = mv2/r
Solve for velocity of a satellite
Solve for the period of the satellite

22. Orbiting objects v = √(GMe/r) T = 2π√(r3/(GMe))
These 2 equations will work for any orbiting body, as long as you put in the right mass for Me and r is the distance between the centers of mass

23. ‘Weightlessness’ Are astronauts weightless?
Find the acceleration due to gravity when the shuttle is in orbit 200 km above the earth’s surface
Weightlessness does not necessarily mean no gravity, freefall creates weightlessness also

24. Tides Moon caused by gravity differences Remember 2! High tides a day
Low tides a day
Spring tides a month
Neap tides a month
seen
explained

25. The strange force Gravity
Gravity, unlike many other forces is not a contact force
What supplies the force?-no string
Gravitational field
Borrows an idea from magnetism and electricity

26. The strange force Gravity
Einstein was not satisfied with field idea
Einstein proposed that gravity was simply a result of curved space

27. The evidence This would require light to be curved by gravity
Demonstrated in 1919 by an eclipse experiment