1. Uniform Circular Motion

2. Uniform circular motion
motion of an object in a circle with a constant or uniform speed
constant change in direction – which means changing velocity

3. Big Bang Theory Physics Lesson Centrifugal vs. Centripetal Force
Leonard Explains Centripetal Force to Penny
Link (go to 2:35 minute mark)

4. Centrifugal vs Centripetal Forces
In common language we have mistakenly been using centrifugal force when we should correctly refer to the phenomenon as centripetal force
Centripetal force is a force that makes a body follow a curved path towards a point as to a center

5. Centrifugal vs Centripetal Forces
Sometimes an outward force is attributed to circular motion.
Centrifugal force represents the effects of inertia that arise in connection with rotation and which are experienced as an outward force away from the center of rotation.

6. Centrifugal vs Centripetal Forces Example of the Lady Bug in a Can

7. Definitions
Period (T in secs - s) : The time it takes for one full rotation or revolution of an object
T = 1 f
Frequency (f in hertz - Hz): The number of revolutions or rotations per unit time.
f = 1 T

8. When an object spins in a circle, the distance it travels in one revolution is the circumference of the circle, 2πr
The time it takes for one revolution is the period, T.
If v = distance traveled t
Therefore circular velocity will be….
vc = 2πr T

9. Uniform Circular Motion: Period
Object repeatedly finds itself back where it started.
The time it takes to travel one “cycle” is the “period”.

10. Quantifying Acceleration: Magnitudev1 v2

11. Quantifying Acceleration: Magnitude
Centripetal Acceleration

12. Applying Newton’s 2nd Law:
Centripetal Force
Always points toward center of circle. (Always changing direction!)
Centripetal force is the magnitude of the force required to maintain uniform circular motion.

13. Direction of Centripetal Force, Acceleration and Velocity
With a centripetal force, an object in motion continues along a straight-line path.
Without a centripetal force, an object in motion continues along a straight-line path.

14. Direction of Centripetal Force, Acceleration and Velocity

15. What if velocity decreases?

16. What if mass decreases?

17. What if radius decreases?

18. What provides the centripetal force?
Tension (with or without elasticity)
Gravity
Friction (on ground) – air resistance negligible
Normal Force
Centripetal force is NOT a new “force”. It is simply a way of quantifying the magnitude of the force required to maintain a certain speed around a circular path of a certain radius.

19. Relationship Between Variables of Uniform Circular Motion
Suppose two identical objects go around in horizontal circles of identical diameter but one object goes around the circle twice as fast as the other. The force required to keep the faster object on the circular path is
the same as
one fourth of
half of
twice
four times
the force required to keep the slower object on the path.
The answer is E. As the velocity increases the centripetal force required to maintain the circle increases as the square of the speed.

20. Relationship Between Variables of Uniform Circular Motion
Suppose two identical objects go around in horizontal circles with the same speed. The diameter of one circle is half of the diameter of the other. The force required to keep the object on the smaller circular path is
the same as
one fourth of
half of
twice
four times
the force required to keep the object on the larger path.
The answer is D. The centripetal force needed to maintain the circular motion of an object is inversely proportional to the radius of the circle. Everybody knows that it is harder to navigate a sharp turn than a wide turn.

21. Relationship Between Variables of Uniform Circular Motion
Suppose two identical objects go around in horizontal circles of identical diameter and speed but one object has twice the mass of the other. The force required to keep the more massive object on the circular path is
the same as
one fourth of
half of
twice
four times
Answer: D.The mass is directly proportional to centripetal force.

22. Tension Can Yield a Centripetal Acceleration:
If the person doubles the speed of the airplane, what happens to the tension in the cable?
Doubling the speed, quadruples the force (i.e. tension) required to keep the plane in uniform circular motion.

23. Friction Can Yield a Centripetal Acceleration:

24. Car Traveling Around a Circular Track
Friction provides the centripetal acceleration

25. Friction Can Yield a Centripetal AccelerationW FN fs
Force X Y W
-mg FN fs
-sFN
Sum ma
What is the maximum speed that a car can use around a curve of radius “r”?

26. Maximum Velocity
Force X Y W
-mg FN FC
-sFN
Sum ma

27. Centripetal Force: Question
A car travels at a constant speed around two curves. Where is the car most likely to skid? Why?
Smaller radius: larger force required to keep it in uniform circular motion.

28. Gravity Can Yield a Centripetal Acceleration:
Hubble Space Telescope
orbits at an altitude of 598 km
(height above Earth’s surface).
What is its orbital speed?

29. Gravity and Centripetal Acceleration:
Centripetal acceleration provided by gravitational force

30. Gravity and Centripetal Acceleration:
Solve for the velocity….

31. Hubble Space Telescope:

32. Banked Curves
Why exit ramps in highways are banked?

33. Banked Curves
Q: Why exit ramps in highways are banked?

34. Banked Curves Q: Why exit ramps in highways are banked?
A: To increase the centripetal force for the higher exit speed.

35. The Normal Force Can Yield a Centripetal Acceleration:
Engineers have learned to “bank” curves so that cars can safely travel around the curve without relying on friction at all to supply the centripetal acceleration.
How many forces are
acting on the car (assuming
no friction)?

36. Banked Curves
Why exit ramps in highways are banked?
FN cosq = mg

37. Banked Curves
Why exit ramps in highways are banked?
FN cosq = mg

38. The Normal Force as a Centripetal Force:
Two: Gravity and Normal
Force X Y W
-mg FN
FNsin
FNcos
Sum ma

39. The Normal Force as a Centripetal Force:

40. The Normal Force and Centripetal Acceleration:
How to bank a curve…
…so that you don’t rely on friction at all!!

41. Artifical Gravity

42. Vertical Circular Motion

43. Vertical Circular Motion

44. Calculations
Practice Set 1 – link
Practice Set 2 - link

45. Acknowledgements
circmotTOC.html

46. The End!