Transcript Chapter 6 Circular Motion

Chapter 6
Circular Motion
and
Other Applications of Newton’s
Laws
Uniform Circular Motion
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A force, Fr , is directed
toward the center of the
circle
This force is associated
with an acceleration, ac
Applying Newton’s
Second Law along the
radial direction gives
v2
 F  mac  m r
Uniform Circular Motion, cont
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A force causing a
centripetal acceleration acts
toward the center of the
circle
It causes a change in the
direction of the velocity
vector
If the force vanishes, the
object would move in a
straight-line path tangent
to the circle
Centripetal Force
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The force causing the centripetal
acceleration is sometimes called the
centripetal force
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This is not a new force, it is a new role
for a force
It is a force acting in the role of a force
that causes a circular motion
Forces that causes centripetal acceleration
We are familiar with different types of forces
such as
Gravity, friction, normal forces and tension etc.
Should we add centripetal forces in this
list?
Answer: No, It is not new kind of
force.
A common mistake in the free body diagram is to draw all usual
forces and then to add another vector for the centripetal force.
But it is not a separate force---it is simply one or more familiar
forces that causes circular motion
Examples
Motion of the earth around the sun:
Gravitational force
An Object sitting on rotating turn table: Friction force
The rock whirled horizontally on the end of string:
string
Tension in the
For an amusement-park Patron pressed against the inner wall of
rapidly rotating room:
normal force exerted by the wall
Conical Pendulum
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The object is in
equilibrium in the
vertical direction and
undergoes uniform
circular motion in
the horizontal
direction
v  Lg sin tan 
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v is independent of
m
The conical Pendulum
Motion in a Horizontal Circle
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The speed at which the object moves
depends on the mass of the object and
the tension in the cord
The centripetal force is supplied by the
tension
Tr
v
m
How fast can it spin
The force cause to the centripetal acceleration is the tension
in the string
Horizontal (Flat) Curve
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The force of static
friction supplies the
centripetal force
The maximum speed at
which the car can
negotiate the curve is
v   gr
Note, this does not
depend on the mass of
the car
What is the maximum speed of the car?
The static friction force enable the car to
move round the circular path
Banked Curve
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These are designed
with friction equaling
zero
There is a component
of the normal force that
supplies the centripetal
force
v2
tan  
rg
The Bank Exit Ramp
Loop-the-Loop
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This is an example
of a vertical circle
At the bottom of the
loop (b), the upward
force experienced by
the object is greater
than its weight
nbot
 v2 
 mg 1  
 rg 
Loop-the-Loop, Part 2
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At the top of the
circle (c), the force
exerted on the
object is less than
its weight
ntop
 v2

 mg   1
 rg 