1. Uniform Circular Motion
Uniform circular motion is motion along a circular path in which there is no change in speed, only a change in direction.
Constant velocity tangent to path. v Fc
Constant force toward center.
Question: Is there an outward force on the ball?

2. Uniform Circular Motion (Cont.)
The question of an outward force can be resolved by asking what happens when the string breaks!
Ball moves tangent to path, NOT outward as might be expected. v
When central force is removed, ball continues in straight line.
Centripetal force is needed to change direction.

3. Examples of Centripetal Force
You are sitting on the seat next to the outside door. What is the direction of the resultant force on you as you turn? Is it away from center or toward center of the turn? Fc
Car going around a curve.
Force ON you is toward the center.

4. The centripetal force is exerted BY the door ON you. (Centrally)
Car Example Continued
The centripetal force is exerted BY the door ON you. (Centrally) F’
Reaction Fc
There is an outward force, but it does not act ON you. It is the reaction force exerted BY you ON the door. It affects only the door.

5. Another Example R Disappearing platform at fair. Fc
What exerts the centripetal force in this example and on what does it act?
The centripetal force is exerted BY the wall ON the man. A reaction force is exerted by the man on the wall, but that does not determine the motion of the man.

6. Spin Cycle on a Washer
How is the water removed from clothes during the spin cycle of a washer?
Think carefully before answering Does the centripetal force throw water off the clothes?
NO. Actually, it is the LACK of a force that allows the water to leave the clothes through holes in the circular wall of the rotating washer.

7. Centripetal Acceleration
Consider ball moving at constant speed v in a horizontal circle of radius R at end of string tied to peg on center of table. (Assume zero friction.) n Fc R v W
Force Fc and acceleration ac toward center. W = n

8. Deriving Central Acceleration
Consider initial velocity at A and final velocity at B: vf vf B R vo
-vo Dv R vo s A

9. Deriving Acceleration (Cont.)vf
-vo R vo Dv s
ac = Dv t
Definition: = Dv v s R
Similar Triangles
mass m = Dv t vs Rt
ac = = vv R
Centripetal acceleration:

10. Car Negotiating a Flat Turnv Fc
What is the direction of the force ON the car?
Ans. Toward Center
This central force is exerted BY the road ON the car.

11. Car Negotiating a Flat Turnv Fc
Is there also an outward force acting ON the car?
Ans. No, but the car does exert a outward reaction force ON the road.

12. Car Negotiating a Flat Turn
The centripetal force Fc is that of static friction fs: R v m Fc n
Fc = fs fs R mg
The central force FC and the friction force fs are not two different forces that are equal. There is just one force on the car. The nature of this central force is static friction.

13. Optimum Banking Angle n n n m
By banking a curve at the optimum angle, the normal force n can provide the necessary centripetal force without the need for a friction force. R v m Fc n
fs = 0 n fs q
slow speed q n fs q w w w
fast speed
optimum

14. The Conical Pendulum
A conical pendulum consists of a mass m revolving in a horizontal circle of radius R at the end of a cord of length L.
T cos q q h T L R T q mg
T sin q
Note: The inward component of tension T sin q gives the needed central force.

15. Solve two equations to find angle q
Angle q and velocity v: q h T L R mg
T sin q
T cos q
Solve two equations to find angle q
mv2 R
T sin q =
tan q = v2 gR
T cos q = mg

16. For Motion in Circle v AT TOP: mv2 R + T = - mg R mg T AT BOTTOM: mv2

17. The Loop-the-Loop Same as cord, n replaces Tv
AT TOP:
n = mg
mv2 R n mg +
AT BOTTOM: n mg +
n= mg
mv2 R

18. The Ferris Wheel n n = mg - n n = + mg R v mg - n = mv2 R AT TOP: mg +
AT BOTTOM: n mg +
n = mg
mv2 R

19. Reminder about the normal force
Centripetal force is not a distinct force.
Centripetal force is NOT one of the forces you draw in the free-body diagram.
Centripetal force is the net force that is directed towards the center of the circular path.

20. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics
Southern Polytechnic State University
© 2007