1. KD4 Projectile and Circular Mechanics Chapter 3; Chapter 9

2. Questions for Thought Which moves faster on a merry-go-round, a horse on the outside or inside? What happens if you are the passenger in a car and the driver takes a right-hand turn? Left-hand turn? What happens during the spin cycle in a washing machine?

3. Rotation vs. Revolution Rotation (spin) – Motion of an object spinning around an internal axis Ex) Merry-go-round spins around its own axis Revolution- Motion of an object turning around an external axis Person on merry-go-round revolves around the same axis

4. Hmmm? Which moves faster a person near the outside of the merry-go-round or one near the inside of the same merry-go-round?

5. Rotational vs. Tangential Speed Rotational speed (angular)-# of rotations/time Both have the same rotational speed Tangential speed (linear)-Distance moved/time The person on the outside has a greater tangential speed because he/she is moving a greater distance

6. Part 1: Circular Motion Uniform Circular Motion-The motion of an object traveling in a circular path at a constant speed Ex) A tetherball moving in a circular path Is the tetherball accelerating?

7. Circular Motion Centripetal acceleration- Acceleration due to changing direction “Center seeking” All objects moving in a circle are accelerating (towards the center)

8. Centripetal Acceleration a = v ² /R a = 2 лv/T a = 4л²R/T² R=Radius T=period (time for 1 revolution)

9. Centripetal Acceleration An object which experiences an acceleration must also experience a force F=ma

10. Centripetal Force Force acting towards the center which causes the object to seek the center Works against inertia

11. What is the Centripetal Force? A car moving around a track? Frictional force between tires and Earth forcing car inward keeping it in its path Planets orbiting the sun? Gravitational force pulling on the object keeps it in its path

12. Centripetal Force Formulas: F c =(m) (a c ) F c = (m) (V 2 /R) F c = (m) (2πv/T) Fc = (m) (4π 2 R/T 2 )

13. Centrifugal Force “Center fleeing” This is a FAKE force Outward force is a misconception due to inertia

14. If swing a can on the end of a string over your head and the string breaks, what happens to the can? The can moves in a straight line tangent to its circular path

15. Example: Calculate the maximum speed a 1200 kg car can travel around a curve of 35 m radius if the frictional force between the tires and the road surface is 2.4 X 10 3 N. Fc = m v 2 / r 2.4 x 10 3 = 1200 v 2 / 35 V = 8.4 m/s

16. Centripetal acceleration is always toward the center Centrifugal acceleration does NOT exist since centrifugal force does NOT exist

17. What happens to a person in the backseat if driver makes a right turn? Left? The person goes STRAIGHT (due to inertia), but you get the misconception you are going outward

18. Part 2: Projectile Motion Motion resulting from the sum of 2 independent velocities Horizontal constant velocity (neglecting air resistance) Vertical increasing velocity (due to gravity)

19. Projectile Motion Makes a parabolic path

20. Projectile Motion: Equations Range (horizontal distance) Constant D x = v x t Altitude (height) Changes due to gravity D y = ½ g t 2 vxvx t

21. Example If a bullet is dropped at the same moment a bullet is shot out of a gun (and they both start at the same height), which bullet hits the ground 1st? They both hit at the same time!

22. Example: If a bullet is fired 20 m above the ground, how long does it take to hit the ground? D y = ½ g t 2 20 = ½ (9.8) t 2 t = 2 s

23. What if the object is fired up at an angle?

24. Horizontal vs. Vertical Vertical velocity changes due to gravity Time calculated would be the same up OR down Horizontal velocity is constant (neglecting air) Time would be the same as down vertically is the object is projected horizontally (only going down) Time would be doubled if the object is projected at an angle (due to the object traveling horizontally for the time up AND the time down