1. Circular Motion:
Forces

2. Centripetal Force
All objects that experience circular motion experience a centripetal force.
The centripetal force is the “center seeking” force. It points to the center of the circle of the motion.

3. Centripetal Force, pt 2
No matter where the object is in the circle, the centripetal force points toward the center.

4. Centrifugal Force
From the object’s frame of reference there is an outward force. This is the centrifugal force.

5. Bucket of Water Swung In A Circle
Is there a force pointing outwards that is keeping the water in the bucket?
If a bucket of water is swung in a circle the water will stay in the bucket even when it is upside down. There is an apparent force that pushes the water to the bottom of the bucket which is called the centrifugal force. It is often called a “fictitious” force because there is no actual force pushing on the water. The centrifugal effect is caused by inertia and centripetal acceleration.

6. Inertia
Force?
No, it’s Inertia

7. Centripetal Force

8. Uniform Circular Motion
A 2.0 kg ball completes 3 revs in 6 seconds. What is Fc?
r = 0.5 m

9. Finding v

10. Fc

11. Centripetal Acceleration

12. Non-Uniform Circular Motion
A ball attached to a string moves in a vertical circle. If v = 5 m/s at the point indicated, what is the total acceleration?
r = 0.5 m

13. Total Acceleration
The total acceleration is the combination of the centripetal acceleration and the tangential acceleration. aC aT

14. Non-Uniform Acceleration, Pt 2FT Fg FT FT FT Fg Fg Fg

15. r = 0.4 m m = 1 kg
What is the min. speed to remain in circular motion? FT Fg
The minimum speed occurs when FT=0

17. Tmax=300 N m = 10 kg r = 0.4m
What is v max. without breaking the rope? FT Fg

18. Roller Coaster
A roller coaster has a circular loop that has a 10.0 m radius. It is desired that the occupants feel an acceleration of 1 g pushing them into the seat at the top of the loop. What is the necessary speed at the bottom of the loop that will allow for this condition at the top? (Assume the roller coaster is frictionless)

19. Model FN Fg K+U at top Just K at bottom
Frictionless=Mechanical Energy Conserved
Person “feels” FN as a force pushing up into seat
K+U at top FN Fg
Just K at bottom

20. To feel a sensation of 1g acceleration into the seat,
FN = Fg

21. Conservation of Mechanical Energy