Centripetal Acceleration and Circular Motion

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Centripetal Acceleration and Circular Motion
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Circular Motion
B
C
A
v
Answer B
A ball is going around in a circle attached to a
string. If the string breaks at the instant
shown, which path will the ball follow?
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Acceleration in Uniform Circular Motion
Acceleration is due to change in direction, not
speed. Since turns toward center, must be a
force toward center.
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Acceleration in Uniform Circular Motion
Draw in forces.
v1
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Common Incorrect Forces

• Acceleration SF ma
• Force of Motion (Inertia not a force)
• Centrifugal Force (wrong object!)
• Centripetal Force (tension, gravity, friction,
  normal)

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Example ball in vertical circle
A ball of mass 2kg is being swung in a vertical
circle with a speed of 10m/s. What is the
tension in the rope at the top of the circle?
Draw in forces.
v110m/s
g
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Example ball in vertical circle
A ball of mass 2kg is being swung in a vertical
circle with a speed of 10m/s. What is the
tension in the rope at the bottom of the circle?
Draw in forces.
g
v110m/s
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Example

• Suppose you are driving through a valley whose
  bottom has a circular shape. If your mass is m,
  what is the magnitude of the normal force FN
  exerted on you by the car seat as you drive past
  the bottom of the hill A. FN lt mg B. FN mg
  C. FN gt mg

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Example roller coaster

• What is the minimum speed you must have at the
  top of a 20 meter roller coaster loop, to keep
  the wheels on the track.

Y Direction F ma Let N 0, just touching
mg
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Summary of Concepts

• Uniform Circular Motion
• Speed is constant
• Direction is changing
• Acceleration toward center a v2 / r
• Newtons Second Law F ma

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