Uniform Circular Motion

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Uniform Circular Motion
What is the object being forced to do as a
unbalanced force is Being applied?
What was the equation for velocity?
Revolution?
What would be the equation For an object
revolving in a circle?
Period?
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What do these numbers represent?
Mercury . . . 88 earth days Venus . . . 225
days Earth . . . 365 days Mars . . . 685 days
Jupiter . . . 12 earth years Saturn . . . 29
years Uranus . . . 84 years Neptune . . . 165
years Pluto . . .
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Calculating T and Velocity
What is a period, and what does it stand for?
What is the period, if takes a merry go round 30
seconds to make 5 revolutions?
A ball with a mass of 3.0kg is whirled by a
student. The distance from the ball to the center
of rotation is 4.0m. The time for one revolution
is 2.0sec. What is the velocity of the ball.
Zena the African warrior revolves a rope with
rocks on the end of it with a radius of
1.5meters. She gets 15 revolutions in 10 seconds
before she lets it go to kill a wambat. How fast
was her weapon moving before she let it go?
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Circular Motion
B
C
A
B Tangent to the Circle
Inertia?
A ball is going around in a circle attached to a
string. If the string breaks at the instant
shown, which path will the ball follow?
http//www.youtube.com/watch?vRWeJWchXosY//
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Types of Weapons that use Tangential Velocity
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FN mg
r
FT Tension Force
m
F ma Fc m (v2 / r)
mw
Uniform Circular motion Is it Accelerating?
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Uniform Circular motion
Uniform circular motion in a horizontal plane
Fc m (v2 / r)
Name 3 events as a result of a cable suddenly
breaking

• Tension suddenly disappears and there is no more
  centripetal force
• Circular motion cannot be maintained.
• The rubber stopper will move with its velocity
  tangent to the circle at the instant the string
  breaks

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Multipliers

• How does changing a variable affect the
  centripetal acceleration? Manipulate the
  formula directly.
• If aC 15 m/s2, what if

• The mass is doubled
• The mass is halved
• The velocity is doubled
• iiii. The velocity is tripled

v. The velocity is halved
vi. The velocity is quartered
vii. The radius is quadrupled
viii.The radius is halved
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Multipliers
How does changing a variable affect the
centripetal acceleration? Manipulate the
formula directly. If FC 15 m/s2, what if

• The mass is doubled
• ii. The velocity is doubled
• iii. The velocity is halved
• iv. The radius is halved

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What is the physical meaning of the formula?
Fc m (v2 / r)
AcV2/r
V2?R/T
TTt/of revolutions

• A Ball with a mass of 3.0kg is whirled overhead
  by a student. The distance from the ball to the
  center of rotation is 4.0m.
• The time for one revolution is 3.0 sec.
• Find the velocity of the ball
• Find the centripetal acceleration
• Find the centripetal force
• Sketch the system, showing the magnitude and
  direction of the ball whirling overhead. Be sure
  to label all forces acting on the ball

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Circular Motion Review

• When we see an object carrying out circular
  motion, we know that there must be force acting
  on the object, directed towards the center of the
  circle.
• When you look at the circular motion of a ball
  attached to a string, the force is provided by
  the tension in the string.
• When the force responsible for the circular
  motion disappears, e.g. by cutting the string,
  the motion will become linear.

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Sample Problem




A 95 kg running back makes a turn on the football
field The halfback sweeps out a path that is a
portion of a circle with a radius of a 12 meters,
the halfback makes a quarter turn around the
circle in 2.1 seconds. Determine the speed,
acceleration, and the centripetal force?
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(No Transcript)
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Circular Motion with Frictionbeing the
Centripetal Force
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Circular Motion and its Connection to Friction

• When you drive your car around a corner you carry
  out circular motion.
• In order to be able to carry out this type of
  motion, there must be a force present that
  provides the required acceleration towards the
  center of the circle.
• This required force is provided by the friction
  force between the tires and the road.
• But remember .. The friction force has a maximum
  value, and there is a maximum speed with which
  you can make the turn.

Required force Mv2/r. If v increases, the
friction force must increase and/or the radius
must increase.
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Lets Think About it?
Rex Things and Doris Locked are out on a date.
Rex makes a rapid right-hand turn. Doris begins
sliding across the vinyl seat (that Rex had waxed
and polished beforehand) and collides with Rex.
To break the awkwardness of the situation, Rex
and Doris begin discussing the physics of the
motion that was just experienced. Rex suggests
that objects which move in a circle experience an
outward force. Thus, as the turn was made, Doris
experienced an outward force that pushed her
towards Rex. Doris disagrees, arguing that
objects that move in a circle experience an
inward force. In this case, according to Doris,
Rex traveled in a circle due to the force of his
door pushing him inward. Doris did not travel in
a circle since there was no force pushing her
inward she merely continued in a straight line
until she collided with Rex. Who is correct?
Argue one of these two positions.
When the turn is made, Doris continues in a
straight-line path this is Newton's first law of
motion. Once Doris collides with Rex, there is
then an unbalanced force capable of accelerating
Doris towards the center center of the circle,
causing the circular motion.
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Circular Motion Problem?

A 2000. kg car rounds a circular turn of radius
25 m. If the road is flat and coefficient of
static friction between the tires and road is
0.70, how fast can the car go without skidding?

A 2000. kg car rounds a circular turn of radius
25 m. If the road is flat and coefficient of
static friction between the tires and road is
0.70, how fast can the car go without skidding?
A 2000kg Car rounds a circular turn of radius of
25m. If the road is flat and coefficient of
static friction between the tires and the road is
.70. How fast can the car go without skidding
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Work
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Questions 2

• You are driving a car with constant speed around
  a horizontal circular track. On a piece of paper,
  draw a Free Body Diagram for the car.
• How many forces are acting on the car? A) 1
  B) 2 C) 3 D) 4 E) 5

Normal
Tension
3 forces, Tension (friction), gravity and the
normal force
Gravity
The net force on the car is A. Zero B. Pointing
radially inward C. Pointing radially outward
B Force of tension is pointing inward
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Question 3

• Davain sits on the outer rim of a merry-go-round,
  and Diego sits midway between the center and the
  rim. The merry-go-round makes one complete
  revolution every two seconds.
• Diegos velocity is

Diego
Davian

• (a) the same as Davians
• (b) Faster than Davians
• Slower than Davians

a V2/r
(C) Diego is slower than the velocity of Davian
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Summary

• Uniform Circular Motion
• Speed is constant
• Direction is changing
• Acceleration toward center a v2 / r
• Newtons Second Law F ma

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Universal law of Gravitation

• Explain Newtons Law of Universal Gravitation.

Formula?
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Gravitational Pull Phenomena

• Explain the inverse-square law that Newton
  determined directly determined the force of
  gravity.

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Relationships
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Multipliers Again? What up!

• How does changing a variable affect the
  gravitational force? Manipulate the formula
  directly.
•  If FG 15 N, what if

• the mass of m1 is doubled
• both masses are halved
• m1 is doubled and m2 is halved
• the distance is tripled
• the distance is halved
• the distance is quartered
• the distance is quadrupled
• the distance is doubled

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Problem?

• Two 10.0 kg bowling balls are 50 m apart. What
  is the gravitational force between these two
  objects? What is the gravitational potential
  energy?

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Two More Problems

• The mass of the Earth is 5.98 x 1024 kg and its
  radius is 6.37 x 106 m. Determine the
  acceleration of gravity on the surface of Earth.
  This answer has to be in newtons.

Calculate the Magnitude of the gravitational
force of attraction that Earth exerts on the moon.