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CHAPTER 5Dynamics of Uniform Circular
MotionUniform Circular Motion
Centripetal Acceleration
Centripetal Force
Satellites in Circular Orbits
Vertical Circular Motion
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Uniform Circular Motion Uniform circular motion is the motion of
an object traveling at a constant speed on a circular path
Period (T) is the time required to make one complete revolution
V = 2 p r / T Magnitude of the velocity vector is
constant, however, the vector changes direction and is therefore accelerating. This is known as centripetal acceleration.
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Centripetal Acceleration Magnitude:
The centripetal acceleration can be calculated by the following
Ac = v2/r
Direction: The centripetal acceleration vector always
points toward the center of the circle and continually changes direction as the object moves.
**The centripetal acceleration is smaller when the radius is larger
Pg 155 #1, 3, pg 156 #1, 5, 9
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Centripetal Force Newton’s second law indicates that when
an object accelerates there must be a net force to create the acceleration. The centripetal force points in the same direction as the acceleration (toward the center) and can be calculated as follows:
Fc = mv2/r Name given to the net force required to
keep an object of mass m, moving at speed v, on circular path of radius r.
Pg 155 #7, pg 156 #13, 15, 21
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Satellites in Circular Orbits
There is only one speed that a satellite can have if the satellite is to remain in orbit with a fixed radius.
For a given orbit, a satellite with a large mass has exactly the same orbital speed as a satellite with a small mass.
See pg 144-145 ex 9 Pg 155 #11, pg 158 #31, 33
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Vertical Circular Motion
There are 4 points in a vertical circle where the centripetal force can be identified. The centripetal force is the net sum of all of the force components oriented/pointing toward the center of the circle. EX pg 151
Pg 155 #15, pg 158 #41, 43, 45, pg 159 # 59