1. Uniform Circular Motion
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2. What do you know?
What does UNIFORM CIRCULAR MOTION look like? Can you give a real world example?
Are things in UNIFORM CIRCULAR MOTION accelerating?
Is there a (non-zero) net force acting on an object engaged in UNIFORM CIRCULAR MOTION?

3. What is Uniform Circular Motion?
Uniform means…
What measurements are UNIFORM?
How do you measure, or compute them?

4. Uniform Circular Motion
Constant speed
Constant radius
Continuous acceleration directed radially toward the center
Speed = circumference/period
S=2pr/T

5. Speed and Period explained…
If a record turns at 33.3 revolutions per minute, or revolutions per second, the period is 1.80 seconds.
A point on the edge of a 12 inch record is 0.15m from the center of the record. It moves at a speed of …
S=2pr/T = 2p (0.15)/1.80 = 0.52m/s

6. Example 1
The blades of a blender are 3.0 cm long. The blender spins at a maximum rate of 80 revolutions per second. Determine the speed of the tips of the blades.

7. Example 2
A 30.0 kg child rides on the edge of a 10.0m diameter carrousel that makes revolutions every 1.00 minutes. Compute the speed of the child.

8. Are object’s experiencing UCM accelerating?

9. What affects the magnitude of the acceleration?????

10. UCM Lab
What is the mathematical relationship between centripetal acceleration (m/s/s) and speed(m/s) for an object undergoing UCM?
Consider: If the independent variable is zero, should the dependent variable be zero?

11. ac vs speed and ac vs radius

12. UCM Lab
What is the mathematical relationship between centripetal acceleration (m/s/s) and speed(m/s) for an object undergoing UCM? (Keep the radius constant)
Consider: If the independent variable is zero, should the dependent variable be zero?

13. PLQ

14. Understanding the Lab
When traveling in a circle, is an object accelerating?
Which way?
What happened to the centripetal acceleration when the speed doubled?

15. Centripetal Acceleration
ac = S2/r

16. EX
An astronaut trainee rides in a “centrifuge” that completes one circle every two seconds. Determine the acceleration of the astronaut if they ride 5.0m from the center.

17. SFc vs Speed
What is the mathematical relationship between centripetal Force (N) and speed(m/s) for an object undergoing UCM? (Keep the radius constant)
Consider: If the independent variable is zero, should the dependent variable be zero?

18. Like here….
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19. Understanding the Lab
What happens to the net centripetal force if speed doubles but the radius stays constant?
What would happen to the net centripetal force if we keep speed constant, but double the radius?
What would happen to the net centripetal force if we keep speed and radius constant, but double the mass of the object?

20. Graphs Showing relationships:

21. Equations for UCM
S=2pr/T
ac = S2/r
SFc = m(S2/r)

22. Ex 1
The blades of a blender are 3.0 cm long. The blender spins at a maximum rate of 80 revolutions per second. Determine the speed and acceleration of the tips of the blades.

23. Ex 2
A 20.0 kg child rides on a carrousel, standing 5.00m from the center. The carrousel makes one revolution every 8.00 seconds. Compute the net force acting on the child. What is the direction of the net force? What type of force would provide the net force?

24. Can a Nissan Leaf perform like a Porsche?

25. What affects the max speed for a car around a curve?

26. UCM Problems, where SFc gets expanded
ID what you must find, and what you know
Draw a FBD
ID the inward force
(Deal with the vertical forces if necessary)
Use SFc = m(S2/r)
Sub and solve

27. Ex1
How fast can a 1200kg car travel around a 100m radius arc if the coefficient of _______ friction is 0.8?
What if the car’s mass doubled, but all other factors remained the same?

28. Ex 2

29. Ex2
The Taz Twister was a ride at Great Adventure that consisted of a round room with carpeted walls. Once the room was up to speed the floor was lowered, but the riders, who felt “pinned to the wall” did not drop with the floor. If the radius of the room was 7.0m, and the coefficient of ______ friction between the riders and the wall was 0.5:
what speed must the riders have to stay “glued to the wall”?
what Period must the ride have?