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

3. 5.1. Uniform Circular Motion

4. 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. 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 = 2  r) divided by the time T:

9. 5.2. Centripetal Acceleration

11. The centripetal acceleration of an object moving with a speed v on a circular path of radius r has a magnitude a c 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 a c 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 centripetal acceleration. 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. Answer: To generate the centripetal force required for the circular motion.