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Understanding Dynamics of Uniform Circular Motion

Explore the concepts of uniform circular motion, including period, speed, centripetal acceleration, and centripetal force. Learn how these principles apply to objects moving in circular paths, such as airplanes and cars.

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Understanding Dynamics of Uniform Circular Motion

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  1. C H A P T E R   5Dynamics of Uniform Circular Motion

  2. C H A P T E R   5Dynamics of Uniform Circular Motion

  3. 5.1. Uniform Circular Motion

  4. 5.1. Uniform Circular Motion Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path.

  5. 5.1. Uniform Circular Motion Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path. The motion of a model airplane flying at a constant speed on a horizontal circular path is an example of uniform circular motion.

  6. Period and Speed

  7. Period and Speed The period T is the time required to travel once around the circle—that is, to make one complete revolution.

  8. Period and Speed The period T is the time required to travel once around the circle—that is, to make one complete revolution. The speed v is the distance traveled (circumference of the circle = 2pr) divided by the time T:

  9. 5.2. Centripetal Acceleration

  10. 5.2. Centripetal Acceleration

  11. 5.2. Centripetal Acceleration The centripetal acceleration of an object moving with a speed v on a circular path of radius r has a magnitude ac given by:

  12. 5.2. Centripetal Acceleration The centripetal acceleration of an object moving with a speed v on a circular path of radius r has a magnitude ac given by: Direction: The centripetal acceleration vector always points toward the center of the circle and continually changes direction as the object moves.

  13. Derivation

  14. The effect of the radius r on the centripetalacceleration. Find the centripetal acceleration at each turn for a speed of 34 m/s.

  15. 5.3. Centripetal Force The centripetal force is the net force required to keep an object of mass m, moving at a speed v, on a circular path of radius r, and it has a magnitude of

  16. 5.3. Centripetal Force The centripetal force is the net force required to keep an object of mass m, moving at a speed v, on a circular path of radius r, and it has a magnitude of Direction: The centripetal force always points toward the center of the circle and continually changes direction as the object moves.

  17. Model Airplane Question: What is the centripetal force for the model airplane flying in the horizontal plane?

  18. Model Airplane Question: What is the centripetal force for the model airplane flying in the horizontal plane?

  19. Model Airplane Question: What is the centripetal force for the model airplane flying in the horizontal plane? Answer: The tension in the guideline is the centripetal force, which pulls the plane inward.

  20. Car on a Flat-Curve Question: What is the centripetal force for a car moving along a cul-de-sac?

  21. Car on a Flat-Curve Question: What is the centripetal force for a car moving along a cul-de-sac?

  22. Car on a Flat-Curve Question: What is the centripetal force for a car moving along a cul-de-sac? Answer: Static frictional force between the road and the tires.

  23. Question:Why do airplanes make banked turn?

  24. Question:Why do airplanes make banked turn? Answer: To generate the centripetal force required for the circular motion.

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