This document provides an overview of circular motion and Newton's law of universal gravitation. It defines key concepts like centripetal acceleration, tangential speed, and centripetal force. Examples are provided to demonstrate how to calculate tangential speed from centripetal acceleration and radius. Newton's law of gravitation defines the gravitational force between objects in terms of their masses and the distance between their centers. Kepler's laws of planetary motion are introduced along with concepts like orbital periods and apparent weightlessness in orbiting spacecraft.

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.