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Uniform Circular Motion in AP Physics

Learn about uniform circular motion, centripetal acceleration, tangential velocity, and more concepts in AP Physics. Explore examples and calculations to deepen your understanding.

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Uniform Circular Motion in AP Physics

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  1. Circular Motion AP Physics C Mrs. Coyle

  2. Circular Motion • Uniform circular motion (constant centripetal acceleration) • Motion with a tangential and radial (centripetal)acceleration

  3. Uniform Circular Motion • Object has a circular path, constant speed. • The velocity is always tangent to the path of the object.

  4. Why is there acceleration in uniform circular motion? Dv = vf– vi a= Dv/ Dt

  5. Centripetal Acceleration • Vector • Always perpendicular to the path of the motion. • Points toward the center of the circle.

  6. Characteristics of UniformCircular Motion • Tangential (linear) Velocity • Frequency • Period • Centripetal Acceleration

  7. Frequency, f :#revolutions per unit time • f = # rev / time Units: • (1/sec)=sec-1=Hertz (Hz) • rpm (#rev/min) • rps (#rev/sec) r

  8. Period • Period T : time for 1 revolution • Unit: sec, min, h • Relating Frequency and period f= 1 T

  9. Tangential Speed in terms of T or f v=2pr/T v=2prf

  10. Example 1 • A boy whirls a stone in a horizontal circle of r=1.5m, 2m above the ground. The string breaks and the stone strikes 10m away. What was the centripetal acceleration during the circular motion? • Answer: 160m/s2

  11. Tangential Acceleration • When v varies. • Motion is not uniform circular motion.

  12. Total Acceleration • Tangential acceleration (vector) Plus • Radial acceleration (vector)

  13. Total Acceleration • Tangential acceleration: • Radial acceleration: • Total acceleration:

  14. Total Acceleration • r, radius vector - q , tangent to the circle

  15. Example 2 (#34) An automobile whose speed is increasing at a rate of 0.6m/s2 travels on a circular road of radius 20m. When the instantaneous speed of the car is 4m/s find: a)the tangential acceleration, b)the centripetal acceleration, c)the magnitude and direction of the total acceleration. Ans: a)0.6m/s2,b)0.8m/s2, c)1m/s2,53.1o

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