1. Circular Motion Chapter 9

2. Circular Motion Axis – is the straight line around which rotation takes place. Internal Axis - is located within the body of the object.

3. Circular Motion Rotation – is the spin around the internal axis. External axis – is outside the body of the object.

4. Circular Motion Linear speed - is distance/time Since the outer edge of on object moving in a circle moves further it has greater linear speed.

5. Circular Motion Tangential speed – is the same as linear speed only with a circular motion.

6. Circular Motion Rotational speed - is the # of rotations/time Tangential speed is approximately equal to radial distance x rotational speed.

7. Circular Motion IN ANY RIGIDLY ROTATING SYSTEM, ALL PARTS HAVE THE SAME ROTATIONAL SPEED.

8. Circular Motion Period (T) is the time it takes for one full rotation or revolution of an object. (measured in seconds)

9. Circular Motion Frequency (f) is the # of rotations or revolutions per unit of time. (measured in Hertz Hz).

10. Circular Motion T = 1/f f = 1/T

11. Circular Motion Every object exerts gravitational force on every other object. The force depends on how much mass the objects have and on how far apart they are. The force is hard to detect unless at least one of the objects has a lot of mass.

12. Circular Motion Gravity is the force that keeps planets in orbit around the sun and governs the motion of the rest of the solar system. Gravity alone holds us to the earth’s surface and explains the phenomenon of the tides.

13. Reminders Velocity is speed and the direction of travel. Acceleration is the rate of change of velocity. Force cause the acceleration of motion. Work is done on an object to change the energy of the object.

14. Some definitions Centripetal means “center seeking” Centrifugal means “center fleeing”

15. Circular Motion Consider a Ferris wheel. The cars on the rotating Ferris wheel are said to be in circular motion.

16. Circular Motion Any object that revolves about a single axis undergoes circular motion. The line about which the rotation occurs is called the axis of rotation. In this case, it is a line perpendicular to the side of the Ferris wheel and passing through the wheel’s center.

17. Tangential speed Tangential speed (v i ) can be used to describe the speed of an object in circular motion. The tangential speed of a car on the Ferris wheel is the car’s speed along an imaginary line drawn tangent to the car’s circular path.

18. Tangential speed This definition can be applied to an object moving in circular motion. When the tangential speed is constant, the motion is described as uniform circular motion.

19. Tangential speed The tangential speed depends on the distance from the object to the center of the circular path.

20. Tangential speed For example, consider a pair of horses side- by-side on a carousel. Each completes one full circle in the same time period, but the horse on the outside covers more distance than the inside horse does, so the outside horse has a greater tangential speed.

21. Centripetal Acceleration Suppose a car on a Ferris wheel is moving at a constant speed around the wheel. Even though the tangential speed is constant, the car still has an acceleration.

22. Centripetal Acceleration a = v f - v i t f - t i ________

23. Centripetal Acceleration Or put in words, centripetal acceleration is equal to linear speed squared divided by the radius.

24. Speed V = (2Πr) / T

25. Centripetal Acceleration Acceleration depends on a change in the velocity. Because velocity is a vector, acceleration can be produced by a change in the magnitude of the velocity, a change in the direction of the velocity, or both.

26. Centripetal Acceleration The acceleration of a Ferris wheel car moving in a circular path and at constant speed is due to a change in direction. An acceleration of this nature is called a centripetal acceleration.

27. Centripetal Acceleration The magnitude of a centripetal acceleration is given by the following equation. Centripetal acceleration = (tangential speed) 2 / radius of circular path

28. Example A test car moves at a constant speed around a circular track. If the car is 48.2 meters from the track’s center and has a centripetal acceleration of 8.05 m/s 2 what is the car’s tangential speed?

29. Solution Given: r = 48.2 m a c = 8.05 m/s 2 Unknown: v t = ?

30. Solution a c = v t 2 / r 8.05 m/s 2 = v t 2 / 48.2 m v t = 19.7 m/s