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
 Onlythe 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 = vt2
r

8. +
Example
 ac = vt2
r
 acr = vt2
 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. +
Centripetal Acceleration
Click below to watch the Visual Concept.
Visual Concept

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?
 Ina straight line, as shown on the
right

12. +
Centripetal Force (Fc)
Fc mac
vt 2
and ac
r
mvt 2
so Fc
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/sr= 188.5 m
 Fc= 1.89X 104 N m= ??

14. +
Example
 Fc = mvt2m = Fcr
r vt2
m = (1.89 X 104)(188.5m)
(56.6)2
m = 1112.09 kg

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?
 Thereis 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).
 Hesolved Newton’s equation for G and
substituted his experimental values.

24. +
Gravitational Force
 Ifgravity 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. +
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.

27. +
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.

28. +
Calculating the value of g
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.
Fg GmmE GmE
g 2 2
m mr r

29. +
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
 Findthe 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

30. +
7.3 Motion in Space
Pg. 248- 253

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

32. +
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

33. +
Kepler’s Laws
Kepler’s third law
 Relatesorbital period (T) to distance from
the sun (r)
 Period is the time required for one revolution.
 Asdistance increases, the period
increases.
 Not a direct proportion
 T2/r3 has the same value for any object orbiting
the sun

34. +
Equations for Planetary Motion
 UsingSI units, prove that the units are consistent for
each equation shown below.

35. +
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

36. +
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.

37. +
Apparent Weightlessness
 Elevator at rest: the scale reads the weight
(600 N).
 Elevatoraccelerates downward: the scale
reads less.
 Elevator
in free fall: the scale reads zero
because it no longer needs to support the
weight.

38. +
Apparent Weightlessness
 Youare falling at the same rate as your
surroundings.
 No support force from the floor is needed.
 Astronautsare in orbit, so they fall at the
same rate as their capsule.
 Trueweightlessness only occurs at great
distances from any masses.
 Even then, there is a weak gravitational force.