1. CENTRIPETAL FORCE Centripetal Force is the force required to change the direction of a moving object. Newton’s 1 st Law version 2.0: An object at rest stays at rest and an object in motion stays in straight line motion unless acted upon by a net force.

2. CENTRIPETAL FORCE So how do we get something to "turn"? We apply a force like this: Perpendicular to the direction of motion

3. CENTRIPETAL FORCE We talk about a “Force”. Recall that where there is a net force, there is ____________

4. CENTRIPETAL FORCE We talk about a “Force”. Recall that where there is a net force, there is Acceleration.

5. CENTRIPETAL FORCE Imagine a ball being spun around in a horizontal circle at a fixed speed: 2.00 m/s. Where is the acceleration? The speed is fixed?

6. CENTRIPETAL FORCE Velocity is a vector: It has speed and direction. If we change speed, we accelerate. If we change direction, we must, by definition, accelerate as well !

7. CENTRIPETAL FORCE Let’s examine how this works: Above is our definition of acceleration. There is no numerical difference, so we need to use vectors to find the directional difference

8. CENTRIPETAL FORCE From the previous page we draw the velocity vectors: v1 v2 We will subtract them vectorially and find the difference…the difference will be  v, our numerator in a =  v/  t

9. CENTRIPETAL FORCE First we have to create a negative v … v1

10. CENTRIPETAL FORCE First we have to create a negative v … v1 -v1

11. CENTRIPETAL FORCE Then we ‘add’ them: -v1 v2

12. CENTRIPETAL FORCE Then we ‘add’ them: -v1 v2

13. CENTRIPETAL FORCE Then we ‘add’ them: -v1 v2 v2-v1 =  v

14. CENTRIPETAL FORCE More importantly, look at the direction of the accelerated motion… It’s pointed directly at the center!

15. CENTRIPETAL FORCE CENTRIPETAL: from Latin centrum "center" and petere "to seek"

16. CENTRIPETAL FORCE Derivation of centripetal acceleration equation:

17. CENTRIPETAL FORCE Derivation of centripetal acceleration equation: -v1 v2 v2-v1 =  v

18. CENTRIPETAL FORCE Derivation of centripetal acceleration equation: -v1 v2 v2-v1 =  v

19. CENTRIPETAL FORCE Derivation of centripetal acceleration equation: -v1 v2 v2-v1 =  v r

20. CENTRIPETAL FORCE Derivation of centripetal acceleration equation: -v1 v2 v2-v1 =  v r r

21. CENTRIPETAL FORCE Derivation of centripetal acceleration equation: -v1 v2 v2-v1 =  v r r x

22. CENTRIPETAL FORCE r r x Derivation of centripetal acceleration equation: -v1 v2 v2-v1 =  v r r x

23. CENTRIPETAL FORCE rr x  -v1v2 vv 

24. CENTRIPETAL FORCE rr x  -v1v2 vv 

25. CENTRIPETAL FORCE Now put this in our equation for acceleration:

26. CENTRIPETAL FORCE

30. So finally we get: CENTRIPETAL ACCELERATION CENTRIPETAL FORCE