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Circular Motion

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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Circular Motion

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  1. Circular Motion

  2. 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

  3. 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).

  4. 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

  5. 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)

  6. 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

  7. 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.

  8. 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

  9. 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. next

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