Circular Motion

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Circular Motion

• Rotation Revolution
• Rotational Speed
• Centripetal Force
• Centrifugal Force

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Uniform Circular Motion

• Uniform circular motion is the motion of an
  object traveling at a constant speed on a
  circular path.
• Circular motion takes place around an axis a
  straight line around which rotation takes place.

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• When the object turns around an internal axis it
  is called rotation, or spin.
• When the object turns around an external axis it
  is called revolution.
• For Example, the Earth rotates around its
  internal axis, while also revolving around the
  Sun.

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Rotational Speed

• Rotational Speed, sometimes called angular speed,
  is the number of rotations per unit of time.
• Example rpm stands for revolutions per minute

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Period (T)

• The period is the time required to travel once
  around the circle.
• (time to make one complete revolution)
• The period is represented by a capital letter
  T.
• The period can be used to find velocity

v 2?r T
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Example 1

• The wheel of a car rotates once every 0.072
  seconds. It has a radius of 0.29 m. Determine
  the velocity at which the outer edge of the wheel
  is moving.

v 2?r T
v 2?(0.29) / 0.072 s v 25 m/s
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Example 2

• Two ladybugs are sitting on a record player.
• One sits close to the center of the record and
  the other sits on the outer edge.
• As the record spins, which ladybug has the
  greater velocity?

The ladybug on the outside has a larger radius
than the ladybug on the inside. Therefore, it
will have a higher velocity than the one on the
inside.
v 2?r T
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Centripetal Acceleration

• If an object is moving in a straight line at a
  constant speed is it accelerating?
• No, there has to be a change in velocity for
  acceleration to occur.
• If an object is moving in a circle at a constant
  speed is it accelerating?
• Yes, because any change in direction causes
  acceleration.

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Finding Centripetal Acceleration (magnitude
direction)

• Magnitude
• ac v2
• r
• Direction The centripetal acceleration vector
  always points toward the center of the circle and
  continually changes direction.

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Example

• A bobsled track contains turns with radii of 33m
  and 24 m. Find the centripetal acceleration at
  each turn for a speed of 34 m/s.

Radius 33 m ac (34 m/s)2 / 33m ac 35 m/s2
Radius 24 m ac (34 m/s)2 / 24 m ac 48 m/s2
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Centripetal Force

• Since a F/m, there must also be a force
  associated with circular motion.
• The net force causing centripetal acceleration is
  called the centripetal force (Fc) and points in
  the same direction as the acceleration (towards
  the center of the circle).

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Finding Centripetal Force

• Magnitude
• Fc mv2
• r
• Direction
• points toward the center of the circle
  continually changes direction.

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Example

• A model airplane is swung in circle on a rope.
  Find the the tension (force) on the rope if the
  plane has a mass of 0.90 kg, the rope is 17 m,
  and the speed is 19 m/s.
• Fc mv2/r
• Fc (0.90kg)(19 m/s)2 / 17m
• Fc 19 N