Download Centripetal Force

Uniform Circular Motion
http://www.physicsclassroom.com/mmedia/circmot/circmotTOC.html
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Uniform circular motion
• motion of an
object in a
circle with a
constant or
uniform speed
• constant
change in
direction
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Uniform Circular Motion: Period
Object repeatedly
finds itself back where
it started.
distance = rate  time
distance 2r
time =

rate
v
2r
T=
v
The time it takes to
travel one “cycle” is
the “period”.
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Quantifying Acceleration: Magnitude
v1
v2
Similar Triangles:
v x

v
x
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Quantifying Acceleration: Magnitude
v v  t

v
r
2
v t
v 
r
v v
a

t
r
2
Centripetal Acceleration
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Applying Newton’s 2nd Law:
F  ma
mv
F
r
2
Centripetal Force
Always points toward center of circle.
(Always changing direction!)
Centripetal force is the magnitude of the force
required to maintain uniform circular motion.
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Direction of Centripetal Force,
Acceleration and Velocity
Without a centripetal
force, an object in
motion continues along
a straight-line path.
Without a centripetal
force, an object in
motion continues along
a straight-line path.
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Direction of Centripetal Force,
Acceleration and Velocity
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What if velocity decreases?
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What if mass decreases?
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What if radius decreases?
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What provides the centripetal force?
• Tension
• Gravity
• Friction
• Normal Force
Centripetal force is NOT a new “force”. It is simply a
way of quantifying the magnitude of the force
required to maintain a certain speed around a circular
path of a certain radius.
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Relationship Between Variables of Uniform
Circular Motion
Suppose two identical objects go around in
horizontal circles of identical diameter but one
object goes around the circle twice as fast as the
other. The force required to keep the faster object
on the circular path is
The answer is E. As the
A. the same as
velocity increases the
B. one fourth of
centripetal force required to
maintain the circle increases
C. half of
as the square of the speed.
D. twice
E. four times
the force required to keep the slower object on the path.13
Relationship Between Variables of Uniform
Circular Motion
Suppose two identical objects go around in
horizontal circles with the same speed. The
diameter of one circle is half of the diameter of
the other. The force required to keep the object
on the smaller circular path is
A. the same as
The answer is D. The centripetal force needed
B. one fourth of to maintain the circular motion of an object is
inversely proportional to the radius of the circle.
C. half of
Everybody knows that it is harder to navigate a
D. twice
sharp turn than a wide turn.
E. four times
the force required to keep the object on the larger
path.
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Relationship Between Variables of Uniform
Circular Motion
Suppose two identical objects go around in horizontal circles of
identical diameter and speed but one object has twice the
mass of the other. The force required to keep the more
massive object on the circular path is
A. the same as
B. one fourth of
Answer: D.The mass is directly
C. half of
proportional to centripetal force.
D. twice
E. four times
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Tension Can Yield a Centripetal Acceleration:
If the person doubles the
speed of the airplane,
what happens to the
tension in the cable?
mv
F = ma 
r
2
Doubling the speed, quadruples the force (i.e.
tension) required to keep the plane in uniform circular
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motion.
Friction Can Yield a Centripetal Acceleration:
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Car Traveling Around a Circular Track
Friction provides the centripetal acceleration
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page 166
65. Friction provides the force needed for a car
to travel around a flat, circular race track.
What is the maximum speed at which a car
can safely travel if the radius of the track is
80.0 m and the coefficient of friction is 0.40?
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Centripetal Force: Question
A car travels at a constant
speed around two curves.
Where is the car most likely to
skid? Why?
mv
F = ma 
r
2
Smaller radius: larger force
required to keep it in uniform
circular motion.
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Why does centrifugal force
not actually exist?
Centrifugal force is believed by some to be
an outward force that exists when an object
is in uniform circular motion. However, if
the centripetal force that keeps an object in
uniform circular motion is suddenly
removed, the object does not fly outward
away from the center of the circle. It moves
along a line tangential to the circle. Thus,
there is no centrifugal force.
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Questions solving:
17 & 18 page 156
Q 36 & 37page 164
Q 61 ,62 ,64 page 166
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Vertical Circular Motion
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66.Page 166 (vertical circular motion)
A carnival clown rides a motorcycle down
a ramp and around a vertical loop. If the
loop has a radius of 18 m, what is the
slowest speed the rider can have at the top
of the loop to avoid falling? Hint: At this
slowest speed, the track exerts no force on the
motorcycle at the top of the loop.
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67. A 75-kg pilot flies a plane in a loop as
shown in Figure 6-15. At the top of the loop,
when the plane is completely upside-down for an
instant, the pilot hangs freely in the seat
and does not push against the seat belt. The
airspeed indicator reads 120 m/s. What is
the radius of the plane’s loop?
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78. A 1.13-kg ball is swung vertically from a
0.50-m cord in uniform circular motion
at a speed of 2.4 m/s. What is the tension in
the cord at the bottom of the ball’s motion?
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Circular Motion Concepts on line Quiz
http://www.batesville.k12.in.us/physics/phynet/me
chanics/circular%20motion/Cir_Mot_Quiz.html
Circular Motion Numerical on line Quiz:
http://www.batesville.k12.in.us/physics/phynet/me
chanics/circular%20motion/cm_num_quiz.html
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The End!
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