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Circular Motion - PowerPoint PPT Presentation


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Circular Motion. Measuring a Circle. Motion in a circle is common. The most important measure is the radius ( r ). We use degrees to measure position around the circle. There are 2 p radians in the circle. This matches 360 °

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measuring a circle
Measuring a Circle
  • Motion in a circle is common.
  • The most important measure is the radius (r).
  • We use degrees to measure position around the circle.
  • There are 2p radians in the circle.
    • This matches 360°
  • The distance around a circle is s = rq, where q is in radians.

s = r q

q

r

period and frequency
Period and Frequency
  • Movement around a circle takes time.
  • The period (T) is the time it takes to complete one revolution around the circle.
  • The frequency (f) is the number of cycles around completed in a time.
    • Cycles per second (cps or Hz)
    • Revolutions per minute (rpm)
  • Frequency is the inverse of period (f = 1/T).
velocity in a circle
Velocity in a Circle
  • Velocity is a vector change in position compared to time.
  • The small change in position on the path is the radius times the change in angle.
  • The magnitude rate of change is

Dr = r Dq

Dq

r

angular velocity
Angular Velocity
  • For circular motion, only the time rate of change of the angle matters.
  • The time rate of change of the angle is called the angular velocity.
    • Symbol (w)
    • Units (rad/s or 1/s = s-1)
cycles or radians
Frequency is measured in cycles per second.

There is one cycle per period.

Frequency is the inverse of the period, f =1/T.

Angular velocity is measured in radians per second.

There are 2p radians per period.

Angular velocity, w = 2p/T.

Angular velocity, w = 2pf.

Cycles or Radians
direction of motion
Direction of Motion
  • In the limit of very small angular changes the velocity vector points along a tangent of the circle.
  • This is perpendicular to the position.
  • For constant w, the magnitude stays the same, but the direction always changes.
acceleration in a circle
Acceleration in a Circle
  • Acceleration is a vector change in velocity compared to time.
  • For small angle changes the acceleration vector points directly inward.

dq

centripetal acceleration
Centripetal Acceleration
  • Uniform circular motion takes place with a constant speed but changing velocity direction.
  • The acceleration always is directed toward the center of the circle and has a constant magnitude.
  • This is called centripetal acceleration.

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