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4.4 Uniform Circular Motion

4.4 Uniform Circular Motion. Uniform Circular Motion. Uniform Circular Motion (UCM) occurs when an object moves in a circular path with a constant speed An acceleration exists since the DIRECTION of the motion is changing This change in velocity is related to an acceleration!!!

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4.4 Uniform Circular Motion

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  1. 4.4 Uniform Circular Motion

  2. Uniform Circular Motion • Uniform Circular Motion(UCM) occurs when an object moves in a circular path with a constant speed • An acceleration exists since the DIRECTION of the motion is changing • This change in velocity is related to an acceleration!!! • The velocity vector is always tangent to the path of the object

  3. Changing Velocity in UCM • The change in the velocity vector is due to the change in direction • The vector diagram shows Dv = vf- vi

  4. Centripetal (Radial) Acceleration • The acceleration is always perpendicular to the path of the motion • The acceleration always points toward the center of the circle of motion • This acceleration is called the Centripetal (Radial) Acceleration!!!

  5. Centripetal Acceleration, 2 • The magnitude of the centripetal acceleration vector is given by (4.15) • The direction of the centripetal acceleration vector is always changing, to stay directed toward the center of the circle of motion

  6. Deriving Eqn 4.15 Centripetal (Radial) Acceleration • Motion in a circle from A to point B. Velocity v is tangent to the circle. • AsΔt  0, Δv v&Δvis in the radial direction

  7. Deriving Eqn 4.15, 2 • a  acis (Radial) Centripetal!!! • Similar triangles: 

  8. Deriving Eqn 4.15, final • AsΔt  0, Δθ  0, A  B, (Δr/Δt) v • Magnitude: (4.15) • Direction:Radially & inward!! • Centripetal  “Toward the center”  “Center-seeking” • Centripetal acceleration: Accelerationtowardthe center!! • aC valways!!

  9. Period & Frequency • A particle moving in UCM of radius r (speed v = constant) • Description in terms of period& frequency • Period (T)time for one revolution (time to go around once), usually in seconds. T= t/n • Frequency (f) number of revolutions (n) per second. f = n/t  T = 1/f & f = 1/T

  10. Period & Frequency, 2 • A particle moving in UCM of radius r&speed v = constant • One Complete Circumference distance around = 2πr time = Period (T=1/f) • The speed of the particle would be the circumference of the circle of motion divided by the period Speed ≡distance/time 

  11. Period & Frequency, final • Therefore, the period is: (4.16) • And the frequency is: (4.16a) • Centripetal acceleration: (4.16b)

  12. Example 4.9 The Centripetal Acceleration of the Earth • Calculate ac of the Earth, assuming it moves in a circular orbit around the Sun. • Note that ac<<g

  13. Material for the Midterm • Examples to Read!!! • None • Homework Problems to be solved in Class!!! • Problem: 28 • Problem: 29

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