1. UNIFORM CIRCULAR MOTION PLANETARY MOTION KEPLER’S LAW

2. Circular Motion
Uniform circular motion is a particle moving at constant speed in a circle.

3. UNIFORM CIRCULAR MOTION
Object traveling around circle at a constant speed.
Constant speed
Changing velocity
Changing acceleration
Changing force

4. UNIFORM CIRCULAR MOTION
VELOCITY
Direction changes constantly
Direction is tangent to circle
Period (T) = time to complete one revolution
Units: s / rev; s / cycle; min / rev ; s
Frequency (f) = number of cycles in a given time
Units: rev / s; cycle / s; s-1; Hertz (hz)
Period is inversely related to frequency

5. UNIFORM CIRCULAR MOTION
ACCELERATION
Centripetal acceleration
Direction is towards the center of the circle
units: m/s/s

6. UNIFORM CIRCULAR MOTION
At any given moment
v is pointing tangent to the circle
ac is pointing towards the center of the circle
If the object suddenly broke from circular motion would travel in line tangent to circle

7. UNIFORM CIRCULAR MOTION
FORCE
Centripetal force
Direction is towards the center of the circle
Not a new force but a net force
NEVER EQUAL TO ZERO
units: Newtons (N)
Fc = mv2 r

9. Answers
Pg 236
3) 1.5 m/s/s
4) 58.4 m
Pg 238
3) 40.0 N
4) 35.0 m/s
Pg 263
1) No (greater r, greater v)
2) Constant speed only changing direction
3) A circle
4) Driving around a circle at constant speed
5) yes; r increases until spring force is great enough to keep obj at a constant radius 6) No, ac is for circular motion 7) Not enough force to keep the object at constant force 8) 7.0 m/s 9) 2.7 m/s 10) 414 kg; 12.1 m/s 11) 62 kg

10. UNIVERSAL GRAVITATIONAL LAW
The force is proportional to each mass and inversely proportional to the square of the distance between the two objects.
Inverse square law
All objects are attracted to one another
F = G m1m2 / d2
G = gravitational constant
= X N m2 / kg2
Units: Newton
Cavendish Torsional Balance

11. INVERSE SQUARE LAW

12. UNIVERSAL GRAVITATIONAL LAW
Accounts for ocean tides
Gravitational difference between the Earth, Moon, and Sun.
2 High Tides and 2 Low Tides
Spring Tides
Earth, Moon, Sun are in a line
New Moon and Full Moon

13. What causes tides?
Tides are created by the imbalance between two forces:
Gravitational force of the Moon and Sun on Earth
If mass increases (), then gravitational force increases ()
If distance increases (), then gravitational force greatly decreases ()
Centripetal (center-seeking) force required to keep bodies in nearly circular orbits

14. Tidal bulges Tide-generating forces produce 2 bulges:
Away from Moon on side of Earth opposite Moon
Toward Moon on side of Earth facing Moon
Earth rotates into and out of tidal bulges, creating high and low tides

15. UNIVERSAL GRAVITATIONAL LAW
Neap Tides
Earth, Moon, Sun are perpendicular to each other
Occurs during quarter Moon
Spring Tides
Earth, Moon, Sun are aligned to each other
Occurs during new and full moon

17. Planetary Motion

19. THIRD LAW OF PLANETARY MOTION
Kepler found a relationship between the time it took a planet to go completely around the sun (T, sidereal year), and the average distance from the sun (R, semi-major axis)…