Dynamics of Uniform Circular Motion

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Chapter 5

• Dynamics of Uniform Circular Motion

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5.1 Uniform Circular Motion
DEFINITION OF UNIFORM CIRCULAR MOTION Uniform
circular motion is the motion of an object
traveling at a constant speed on a circular path.
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5.1 Uniform Circular Motion
Let T be the time it takes for the object
to travel once around the circle.
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5.2 Centripetal Acceleration
In uniform circular motion, the speed is
constant, but the direction of the velocity
vector is not constant. Therefore, this means
that an acceleration is occurring. It is given by
The direction of the centripetal acceleration is
towards the center of the circle
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5.3 Centripetal Force
Recall Newtons Second Law When a net external
force acts on an object of mass m, the
acceleration that results is directly
proportional to the net force and has a magnitude
that is inversely proportional to the mass. The
direction of the acceleration is the same as the
direction of the net force.
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5.3 Centripetal Force
Thus, in uniform circular motion there must be a
net force to produce the centripetal
acceleration. 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.
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5.4 Banked Curves
On an unbanked curve, the static frictional
force provides the centripetal force.
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5.4 Banked Curves
On a frictionless banked curve, the centripetal
force is the horizontal component of the normal
force. The vertical component of the normal
force balances the cars weight.
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5.4 Banked Curves
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5.4 Banked Curves
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5.4 Banked Curves
Example 8 The Daytona 500 The turns at the
Daytona International Speedway have a maximum
radius of 316 m and are steely banked at
31 degrees. Suppose these turns were
frictionless. At what speed would the cars have
to travel around them?
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Problems to be solved

• 5.10, 5.23, 5.30, 5.41, 5.50, 5.60
• B5.1 A woman runs on a circular track of radius
  100m at a speed of 8m/s. What is her
  acceleration? Ans 0.64m/s2
• B5.2 A racing car rounds a turn at 60m/s. If the
  force needed to provide the centripetal
  acceleration is equal to the weight of the car,
  what is the radius of the turn? Ans 367.35m

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• B5.3 A car is travelling around a flat curve of
  radius 0.25km. The coefficient of static
  friction between the tires and the road is 0.4.
  At what speed will the car begin to skid? Ans
  31.30m/s
• B5.4 A racing car travels around a curve of
  radius 1000m. If the frictional force is zero and
  the speed is 50m/s, at what angle is the curve
  banked? Ans 14.310