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5/26/2018 5 Uniform Circular Motion
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Chapter 5
Dynam ics of Uni formCircu lar Mot ion
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Uniform Circular Mot ion
DEFINITION OF UNIFORM CIRCULAR MOTION
Uniform circular motion is the motion of an object
traveling at a constant speed on a circular path.
vr
T
2
Let Tbe the time it takes for the object to
travel once around the circle.
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Centr ipetal A ccelerat ion
The direction of the centripetal acceleration is towards the
center of the circle; in the same direction as the change in
velocity.
rva
c
2
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Centr ipetal A ccelerat ion
Example: The Effect of Radius on Centripetal Acceleration
The bobsled track contains turns
with radii of 33 m and 24 m.Find the centripetal acceleration
at each turn for a speed of
34 m/s. Express answers as
multiples of .sm8.9 2
g
gac 6.3
gac 9.4
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Centr ipetal Force
The centripetal force is the name given to the net force
required to keep an object moving on a circular path.
The direction of the centripetal force always points toward
the center of the circle and continually changes direction
as the object moves.
rvmmaF cc
2
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Centr ipetal Force
The Effect of Speed on Centripetal Force
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Centr ipetal Force
A Trapeze Act
In a circus, a man hangs upside down from a trapeze, legs
bent over and arms downward, holding his partner. Is it harderfor the man to hold his partner when the partner hangs
straight down and is stationary or when the partner is swinging
through the straight-down position?
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Satel l i tes in Circular Orbits
There is only one speed that a satellite can have if the
satellite is to remain in an orbit with a fixed radius.
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Satel l i tes in Circular Orbits
Global Positioning System
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Satel l i tes in Circular Orbits
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Apparent Weight lessn ess and A rt i f ic ia l Gravity
Apparent Weightlessness and Free Fall
In each case, what is the weight recorded by the scale?
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Apparent Weight lessn ess and A rt i f ic ia l Gravity
Artificial Gravity
At what speed must the surface of the space station move
so that the astronaut experiences a push on his feet equal to
his weight on earth? The radius is 1700 m.
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Samp le problems for uni form circu lar mo t ion
Example 1 A car has a lateralaccelerationof0.87g. This represents the maximum
centripetal acceleration that can be attained
without skidding out of the circular path. If acar is travelling at a constant 40m/s, what is
the minimum radius of curve it can
negotiate?
Answer: R=190m
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Samp le problems for uni form circu lar mo t ion
Example 2 In a carnival ride, the passengerstravel at a constant speed in a circle of
radius 5.0m. They make one complete circle
in 4.0s. What is their acceleration?
Answer: arad=12m/s2
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Samp le problems for uni form circu lar mo t ion
Example 3 A sled with a mass of 25.0kg rests on a horizontalsheet of frictionless ice. It is attached by a 5.00-m rope to a
post set in the ice. Once given a push, the sled revolves
uniformly in a circle around the post. If a sled makes one
complete revolution in 12.0s, find the force F exerted on it
by the cord.
Answer: F=34.3 N
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