Physics 2211 Todays Agenda

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Physics 2211Todays Agenda

• Acceleration in Uniform Circular Motion
• acceleration
• Dynamics

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Physics 2211Todays Agenda

• Problem 2. An airplane has a cruising speed of
  150 mi/h in calm air. The pilot finds that if he
  sets a compass heading of 10? south of east, it
  takes him 20 min to fly to a point that is 60 mi
  due east of his starting point. If east is
  assumed to be in the positive x direction (and
  north in the positive y direction), what is the
  direction of the wind?
• (a) 39?
• (b) 54?
• (c) 49?
• (d) 44?
• 30?
• answer (a)

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Acceleration in Uniform Circular Motion (UCM)

• Even though the speed is constant, velocity is
  not constant since the direction is changing
  must be some acceleration!
• Consider average acceleration in time ?t
  aav ?v / ?t

v2
R
v1
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Direction of acceleration
If speed is constant, acceleration always point
to the center of the circle
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(No Transcript)
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Acceleration in UCM

• This is called Centripetal Acceleration.
• Now lets calculate the magnitude

?v
v1
v2
But ?R v?t for small ?t
v2
R
So
v1
?R
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Centripetal Acceleration

• UCM results in acceleration
• Magnitude a v2 / R
• Direction (toward center of circle)

R
a
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Motion in a Circle...

• CENTRIPETAL ACCELERATION a v2 / R
• SO THE CENTRIPETAL FORCE IS
• ma mv2 / R
• FNET ma
• mv2 / R

v
y
FNET
R
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Problem Motion in a Circle

• A boy ties a rock of mass m to the end of a
  string and twirls it in the horizontal plane. The
  distance from his hand to the rock is R. The
  speed of the rock is constant and equal to v.
• What is the tension T in the string?

v
T
R
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Motion in a Circle...

• Draw a Free Body Diagram (pick y direction to
  be down)
• We will use FNET ma (surprise)
• First find FNET in y direction
• FNET T
• PROBLEM
• We dont know T!
• We do know object is
• moving in a circle
• with speed v
• How do we use this information?

y
T
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Motion in a Circle...

• CENTRIPETAL ACCELERATION a v2 / R
• SO THE CENTRIPETAL FORCE IS
• ma mv2 / R
• FNET ma
• T mv2 / R

v
y
T
R
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Problem Rotating puck weight.

• A mass m1 slides in a circular path with constant
  speed v on a horizontal frictionless table. It
  is held at a radius R by a string threaded
  through a frictionless hole at the center of the
  table. At the other end of the string hangs a
  second mass m2.
• What is the tension (T) in the string?
• What is the speed (v) of the sliding mass?

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Problem Rotating puck weight...
T

• Draw FBD of hanging mass
• Since R is constant, a 0.
• so T m2g

m2
m2g
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Problem Rotating puck weight...
T m2g
N
T m2g

• Draw FBD of sliding mass

m1
Use F T m1a where a v2 / R
m1g
m2g m1v2 / R
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Recap of Todays lecture

• Circular Motion
• Centripetal Force
• Motion in a vertical circle