1. +
Chapter 7
Pg. 232-261

2. +
7.1 Circular Motion
Pg. 234- 239

3. +
Circular Motion
Any object that revolves about a single
axis
The line about which the rotation occurs is
called the axis of rotation

4. +
Tangential Speed (vt)
Speed of an object in circular motion
Uniform circular motion: vt has a
constant value
Only the direction changes
Example shown to the right
How would the tangential speed of a horse
near the center of a carousel compare to
one near the edge? Why?

5. +
Centripetal Acceleration (ac)
Acceleration directed toward the
center of a circular path
Acceleration is a change in
velocity (size or direction).
Direction of velocity changes
continuously for uniform circular
motion.

6. +
Centripetal Acceleration (magnitude)
How do you think the magnitude of the
acceleration depends on the speed?
How do you think the magnitude of the
acceleration depends on the radius of the
circle?

7. +
Example
A test car moves at a constant speed around a
circular track, If the car is 48.2m from the
center and has the centripetal acceleration of
8.05m/s2, what is the car’s tangential speed?
ac = vt
2
r

8. +
Example
ac = vt
2
r
acr = vt
2
vt =√ac r
vt= √(8.05) (48.2)
vt= 19.69 m/s

9. +
Tangential Acceleration
Occurs if the speed increases
Directed tangent to the circle
Example: a car traveling in a circle
Centripetal acceleration maintains the circular
motion.
 directed toward center of circle
Tangential acceleration produces an increase or
decrease in the speed of the car.
 directed tangent to the circle

10. +
Click below to watch the Visual Concept.
Visual Concept
Centripetal Acceleration

11. +
Centripetal Force
Maintains motion in a circle
Can be produced in different ways,
such as
Gravity
A string
Friction
Which way will an object move if the
centripetal force is removed?
In a straight line, as shown on the
right

12. + Centripetal Force (Fc)
c c
F ma

2
and t
c
v
a
r

2
so t
c
mv
F
r


13. +
Example
A pilot is flying a small plane at 56.6 m/s in a
circular path with a radius of 188.5m. The
centripetal force needed to maintain the plane’s
circular motion is 1.89 X 104 N. What is the
plane’s mass?
Given:
vt= 56.6 m/s r= 188.5 m
Fc= 1.89X 104 N m= ??

14. +
Example
 rearranged
m = (1.89 X 104)(188.5m)
(56.6)2
m = 1112.09 kg
2
t
c
mv
F
r
 2
c
t
F r
m
v


15. +
Describing a Rotating System
 Imagine yourself as a passenger in a car turning
quickly to the left, and assume you are free to move
without the constraint of a seat belt.
 How does it “feel” to you during the turn?
 How would you describe the forces acting on you during this
turn?
 There is not a force “away from the center” or
“throwing you toward the door.”
 Sometimes called “centrifugal force”
 Instead, your inertia causes you to continue in a
straight line until the door, which is turning left, hits
you.

16. +
7.2 Newton’s Law of Universal
Gravitation Pg. 240-247

17. +
Gravitational Force
The mutual force of attraction between
particles of matter.
Gravitational force depends on the
masses and the distance of an object.

18. +
Simpson’s Video
http://www.lghs.net/ourpages/users/dburn
s/ScienceOnSimpsons/Clips_files/3D-
Homer.m4v

19. +
Family Guy Video

20. +
Newton’s Thought Experiment
What happens if you fire a cannonball horizontally
at greater and greater speeds?
Conclusion: If the speed is just right, the
cannonball will go into orbit like the moon,
because it falls at the same rate as Earth’s surface
curves.
Therefore, Earth’s gravitational
pull extends to the moon.

21. + Law of Universal Gravitation
Fg is proportional to the product of the masses
(m1m2).
Fgis inversely proportional to the distance
squared (r2).
 Distance is measured center to center.
G converts units on the right (kg2/m2) into force
units (N). G = 6.673 x 10-11 N•m2/kg2

22. +
Law of Universal Gravitation

23. +
The
Cavendish
Experiment
Cavendish found the value for G.
He used an apparatus similar to that shown
above.
He measured the masses of the spheres (m1 and
m2), the distance between the spheres (r), and
the force of attraction (Fg).
He solved Newton’s equation for G and
substituted his experimental values.

24. +
Gravitational Force
If gravity is universal and exists between
all masses, why isn’t this force easily
observed in everyday life? For example,
why don’t we feel a force pulling us
toward large buildings?
The value for G is so small that, unless at
least one of the masses is very large, the
force of gravity is negligible.

25. +
Ocean Tides
What causes the tides?
How often do they occur?
Why do they occur at certain times?
Are they at the same time each day?

26. +

27. +
Ocean Tides
 Newton’s law of universal gravitation is used to explain the
tides.
 Since the water directly below the moon is closer
than Earth as a whole, it accelerates more rapidly
toward the moon than Earth, and the water rises.
 Similarly, Earth accelerates more rapidly toward the
moon than the water on the far side. Earth moves
away from the water, leaving a bulge there as well.
 As Earth rotates, each location on Earth passes
through the two bulges each day.

28. +
Gravity is a Field Force
Earth, or any other mass,
creates a force field.
Forces are caused by an
interaction between the
field and the mass of the
object in the field.
The gravitational field (g)
points in the direction of
the force, as shown.

29. +
Calculating the value of g
2 2
g E E
F Gmm Gm
g
m mr r
  
Since g is the force acting on a 1 kg
object, it has a value of 9.81 N/m (on
Earth).
The same value as ag (9.81 m/s2)
The value for g (on Earth) can be
calculated as shown below.

30. +
Classroom Practice Problems
Find the gravitational force that Earth
(mE= 5.97  1024 kg) exerts on the moon
(mm= 7.35  1022 kg) when the distance
between them is 3.84 x 108 m.
 Answer: 1.99 x 1020 N
Find the strength of the gravitational field at a
point 3.84 x 108 m from the center of Earth.
 Answer: 0.00270 N/m or 0.00270 m/s2

31. +
7.3 Motion in Space
Pg. 248- 253

32. +Kepler’s Laws
Johannes Kepler built his ideas on
planetary motion using the work of others
before him.
Nicolaus Copernicus and Tycho Brahe

33. +
Kepler’s Laws
Kepler’s first law
Orbits are elliptical, not circular.
Some orbits are only slightly elliptical.
Kepler’s second law
Equal areas are swept out in equal time
intervals.
Basically things
travel faster when
closer to the sun

34. +
Kepler’s Laws
Kepler’s third law
Relates orbital period (T) to distance from
the sun (r)
 Period is the time required for one revolution.
As distance increases, the period
increases.
 Not a direct proportion
 T2/r3 has the same value for any object orbiting
the sun

35. +
Equations for Planetary Motion
 Using SI units, prove that the units are consistent for
each equation shown below.

36. +
Classroom Practice Problems
A large planet orbiting a distant star is
discovered. The planet’s orbit is nearly
circular and close to the star. The orbital
distance is 7.50  1010 m and its period is
105.5 days. Calculate the mass of the star.
 Answer: 3.00  1030 kg
What is the velocity of this planet as it orbits
the star?
 Answer: 5.17  104 m/s

37. +
Weight and Weightlessness
Bathroom scale
A scale measures the downward force
exerted on it.
Readings change if someone pushes down
or lifts up on you.
 Your scale reads the normal force acting on you.

38. +
Apparent Weightlessness
Elevator at rest: the scale reads the weight
(600 N).
Elevator accelerates downward: the scale
reads less.
Elevator in free fall: the scale reads zero
because it no longer needs to support the
weight.

39. +
Apparent Weightlessness
You are falling at the same rate as your
surroundings.
 No support force from the floor is needed.
Astronauts are in orbit, so they fall at the
same rate as their capsule.
True weightlessness only occurs at great
distances from any masses.
 Even then, there is a weak gravitational force.