Download Circular Motion

Dynamics of Uniform Circular Motion
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Dynamics of Uniform Circular Motion
• Uniform circular motion is the motion of an
object traveling at a constant speed on a
circular path
• The period T is the time required for the
object to travel once around the circle
• The speed v of the object is related to the
period and the radius of the circle by
C (circumference)  2 r   d
2 r
v
T
– Example 1 and 2
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Dynamics of Uniform Circular Motion
• Centripetal Acceleration
– An object in uniform circular motion experiences an
acceleration (even at constant velocity...because its
direction is changing), known as centripetal acceleration.
The magnitude of the centripetal acceleration is 2
v
ac 
r
– where v is the speed of the object, and r is the radius of
the circle. Example 3
ac is always
pointing toward the
center of the circle
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Dynamics of Uniform Circular Motion
• Centripetal Force
– To produce a centripetal acceleration, a net
force pointing towards the center of the circle
is needed…remember……F=ma....a=F/m
–
– where m is the mass of the object, v is the
speed of the object, and r is the radius of the
circle.
As v increases, so
will the tension in
the string (Fc)
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NOTES about Dynamics of Uniform Circular Motion
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Dynamics of Uniform Circular Motion
•
•
Centripetal force and Centrifugal force are the action-reaction force
pair associated with circular motion.
According to Newton's first law of motion, a moving body travels along
a straight path with constant velocity unless it is acted on by an
outside force.
– For circular motion to occur there must be a constant force acting on a
body, pushing it toward the center of the circular path
• This force is the centripetal (“center-seeking”) force
– For a planet orbiting the sun, the force is gravitational
– an object twirled on a string, the force is mechanical
– for an electron orbiting an atom, it is electrical
• According to Newton's third law of motion, for every action there is an equal and
opposite reaction. The centripetal force, the action, is balanced by a reaction
force, the centrifugal (“center-fleeing”) force. The two forces are equal in
magnitude and opposite in direction. The centrifugal force does not act on the
body in motion; the only force acting on the body in motion is the centripetal
force.
• The centrifugal force is often mistakenly
thought to cause a body to fly out of its
circular path when it is released; rather, it is
the removal of the centripetal force that
allows the body to travel in a straight line as
required by Newton's first law.
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Applications of Dynamics of Uniform Circular Motion
• Banked Curves
FN is normal to the surface and is the force that the road applies to the car
FN has a component FN sin  that pushes towards the center and provides the centripetal force
mv 2
FC  FN sin  
r
• The components of the normal force
FN cos  must balancethe weight mg therefore
FN cos   mg dividing this equation in to the previous
FN sin  mv 2

FN cos 
r
•

v2
tan  
rg
Do example 8
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Vertical Circular Motion and Roller Coasters!
mv 2
F  r
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