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.
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
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
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
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.