Physics 135A

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Physics 135A

• Physics 135A
• Lecture 7 Circular Motion
• Dr. Z. Gong

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Physics 135A
Administrative Information

• Homework Set 3 due on Thursday

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Physics 135A
Review -1

• Free Body Diagram
• Separate each object and draw all the forces
  acting on each object of interest
• Set up coordinate axes, and then get the x and y
  components of all the forces
• Apply Newtons second law of motion on each axis,
  separately.

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Physics 135A
Review -2

• Static friction force parallel to the surface
  of contact, when there is no relative motion
  between the 2 objects
• Static friction force Ffr can vary from zero to
  FmaxµsFN where µs is coefficient of static
  friction and FN is the normal force
• Static friction force is against the tendency of
  motion

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Physics 135A
Review -3

• Kinetic friction force parallel to the surface
  of contact when there is relative motion between
  the 2 objects
• Kinetic friction force keeps
  the same if theres no change on the normal force

30o
30o
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Physics 135A
Uniform Circular Motion

• Uniform circular motion An object moves in a
  circle at constant speed

• Period T the time it takes to revolve a circle
• Frequency f number of revolutions per second

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Physics 135A
Velocity Change

• Velocity is vector velocity is changing when
• The magnitude of velocity is changing, like in
  free fall
• The direction of velocity is changing, like in
  uniform circular motion

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Physics 135A
Centripetal Acceleration and Force

• Centripetal acceleration
• Centripetal force
• The centripetal force is pointing to the center
  of the circle.

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Physics 135A
Example -1

• If a tetherball of mass m is circling around a
  pole at an angle of ? by a string l, what is the
  centripetal force and the speed of the ball?
• What is the horizontal
• component of the tension force
• FTx do?
• It is the centripetal force to
• hold the tether ball in circular
• motion.

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Physics 135A
Example -1
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Physics 135A
Example -2

• What is the minimum speed a bucket of water m
  needs to circulate vertically at a radius r
  without spilling out?
• Free body diagram

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Physics 135A
Example -2

• If the cord is cut when the bucket reaches A at
  vmin how far will it fly before it reaches the
  ground?

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Physics 135A
Example -3

• A car is turning at radius R on an incline bank
  of angle ?. If the coefficient of static friction
  is µ, what is the minimum and maximum speed the
  car can move without sliding up or down?

?
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Physics 135A
Example -3

• If the car is too slow then it has the tendency
  to slide downward. The friction force is pointing
  upward.

?
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Physics 135A
Example -3
?
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Physics 135A
Example -3

• If the car is too fast then it has the tendency
  to slide upward. The friction force is pointing
  downward.

?
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Physics 135A
Example -3
?
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Physics 135A
Example -3

• This example includes both circular motion and
  friction force.
• In order to prevent the car from sliding upward
  or downward, its speed must be between

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Physics 135A
Non-uniform Circular Motion

• Both the direction and the magnitude of the
  velocity are changing