1. Chapter 9- Circular Motion

2. AXIS OF ROTATION
This is an imaginary line through the center of the spinning
The points on the axis of rotation don’t move due to the spinning

3. As the circle spins the point on the axis of rotation appears is still

4. As the circle spins the point on the axis of rotation appears is still

5. Here the axis of rotation is not in the center, where is it?

6. If the axis of rotation is through the object it is called
If the axis of rotation is outside of the object it is called REVOLUTION

7. The earth rotates and revolves

8. The earth rotates and revolves

10. Does a figure skater rotate or revolve
As they spin?

11. “Normal” or linear speed
Slow
Fast
Rotational speed
Slow
Fast

12. Linear speed is the distance moved divided by the time
Rotational speed is the number of complete rotations divided by the time
rotations s

13. The most common unit of rotational speed
rotations
Rotations Per Minute
min
RPM’s
Where have you heard of RPMs

14. A record player makes 100 complete spins in 25 s seconds what is its rotational speed?
Could an object have a rotational speed of .75 rot/s. What would it mean?

15. A typical DVD player spins a DVD at about 900 RPM
How many times does it spin around in 1 second?
How many rotations does it make in 10.5 s?

16. The speed (in m/s) of an object in a circular path is called its
Tangential Speed, vt
Its direction is always tangent to the circular path

17. Compare rotational speed of each dot.
They both complete 1 rotation in the same amount of time

18. Compare their tangential speeds
The outer dot has to move faster in order to travel the longer path in the same amount of time

19. Both dots have the same rotational speed
But different tangential speeds
The tangential speed depends on what?
HOW FAR THE POINT IS AWAY FROM…..
The axis of rotation
This is called its radial distance

20. Do the records have the same rotational speed?
Do the dots have the same tangential speed?
Do the dots have the same radial distance?

21. vt = r w Tangential Speed Rotational speed* Radial distance
*In order for the number to work out,
the rotational speed has to be in radians/sec

22. v = r w
A spot moves fastest on a record which is spinning fast and is far away from the center
If the record doubles its rotational speed, the tangential speed of an object…

23. v = r w
If the blue dot is twice as far from the center as the red dot then it tangential speed is __________
twice as much

24. Where is the axis of rotation?
30 cm
90 cm
Where is the axis of rotation?
If the 30 cm mark is moving at 2 m/s, how fast is the 90 cm mark moving?

25. A record player spins at 5 rpm’s.
One penny is placed 1 cm away from the center of the record and has a tangential speed of 2 m/s. What will be the rotational and tangential speed of a penny placed at 3 cm away from the center?

26. The points travel the circumference of a circle.
What is the distance traveled by each dot if the disk makes 1 rotation?
.75 m
.20 m
What is the tangential speed of the blue dot if the disk has a rotational speed of 1.0 rotation per second?
3 rps?
The points travel the circumference of a circle.

27. For the most excitement where do you want to be on this ride
For the most excitement where do you want to be on this ride? A horse close to the middle or towards the edge?

28. A wheel can both rotate and move (linearly)
Rotating
moving linearly

29. A wheel which is rolling along the ground both moves linearly and rotates at the same time.

30. How far does a wheel move across the ground if it makes 1 rotation
How far does a wheel move across the ground if it makes 1 rotation? Any guesses

31. If the wheel doesn’t skid, as the wheel makes 1 rotation
If the wheel doesn’t skid, as the wheel makes 1 rotation. If will move a distance equal to its circumference

32. A wheel on a bicycle travels 4 m across a road
A wheel on a bicycle travels 4 m across a road. If the radius of the wheel is 0.25 m, how many rotations did the tire make?
If the bike crossed the road in 5 seconds, what was the angular speed of the wheel and the linear speed of the bike?

33. Book problems
Page 133 – 135
#’s 2, 4, 5, 6, 20
A car wheel with a radius of 0.34 m, rotates 4.5 times. How far did the car travel?
How many rotations does a cup make as it travels 1.0 m across a desk. The cup radius is 12 cm?

34. Rotation and cups activity

35. Train track demo
To keep the train centered on its tracks which is the best design?

36. Train track demo
Note that the wheel is like the tapered cup. Which side of the wheel will go faster?
When the rails get unaligned, which will self-correct?

37. Train track demo
How will that cause each train to turn?

38. Train track demo
Which one keeps the train on the tracks?

39. The differential gear allows a car to turn more easily
The outer wheel has to travel a greater distance and tries to spin the axles at more RPM’s
animation of a differential gear

40. What direction is the force?
What causes it to accelerate?
Does the ball accelerate?

41. Is it accelerating?
Does the speed of the ball change?
In what direction is the force acting?

42. The velocity of an object moving about in a circle changes (even if its speed is constant)
What does the arrow represent?

43. This force only changes the direction not the speed. Can you see why?
It is always perpendicular to the velocity

44. This inward force is called a centripetal force
A Centripetal force causes an object to travel in a circle at a constant speed.
Centripetal means “center-seeking” FC vt
Does a centripetal force do work on an object?

45. A centripetal force is NOT a “new” type of force like FN, FF, FG, FT
It is simply one of the above acting in such a way to make an object travel in a circle.
But how does it “Know” to always point to the center, it must be COMPLICATED???

46. The centripetal force is always perpendicular to the velocity!
ball on a string demo
What is the centripetal force?
How does it always point to the middle?
The centripetal force is always perpendicular to the velocity!

47. What provides the centripetal force in the scenarioFg

48. What provides the centripetal force on the penny that keeps in moving in a circle on a record?FF

49. FN What provides the centripetal force in the scenario
That keeps the riders moving in a circle? FN

50. FN Fg What forces do you experience on a merry go round as it spins?
It feels like a force is pushing you to the outside of the circle, what is the dealer of this force?

51. Assume there is NO gravity
If the string were to be cut what path would the ball take? B A C D E F
Assume there is NO gravity

52. Anything curved has to go if no force is acting on the ball

53. Anything curved has to go if no force is acting on the ball

54. Let’s try it and find out?

55. What direction was the ball headed just before the string broke

56. What direction was the ball headed just before the string broke

57. Back to the rotor ride. You feel pressed against the wall
Back to the rotor ride. You feel pressed against the wall. What force does this?
Indicate all of the forces acting on the person. Fg FN FF
There is NO FORCE pushing the person outward from the center of rotation!!!
What is the Net force acting on the person?

58. Driving a car
speeding up, slowing down, making a turn

59. INERTIA Ignoring gravity the only force on the ball is the string.
If the string is cut there are no forces on the ball, and it just moves in a straight line at a constant speed due to …..
INERTIA

60. The only force is directed inward
There is NO outward directed force referred to as centifugal force it only feels like it.
Centripetal force
(tension)

61. An overhead view of a car on a circular track, what provides the centripetal force

62. What happens if friction is lost?

63. The wall must constantly push you towards the circle, fighting your inertia to move in a straight line
If the walls suddenly vanished which way would you fly?
When you are in a spinning ride it feels like you are being PRESSED against the walls by a “Force” FN

64. Centripetal Force Activity

65. The faster an object goes around in a circle, the more centripetal force is needed.

66. Think back to being in an elevator.
Depending on your movement, you have feel heavier or lighter than normal.

67. If you were in a rotating spaceship, the “floor” would constantly be pushing against your feet to keep you moving in a circle
From your perspective what direction would this normal force point?

68. The floor would always be pushing “UP”
Is there something pushing you “DOWN”
ARTIFICIAL GRAVITY!!!!!
NO but it would FEEL like it.

69. All other things the same, which object will need more centripetal force
A faster velocity increases the FC needed

70. How could you increase the artificial gravity on this spaceship?

71. If an object is moving fast and makes a sharp a lot of centripetal force is needed.

72. Compare the artificial gravity felt by each person
Compare the tangential speeds
Compare the rotational speeds
The further away from the axis of rotation, the greater the centripetal force primarily because…
They are moving faster

73. When the record is spun faster which penny will fly off first?

74. Swinging a ball on a string
Just the right amount of centripetal force is needed to keep an object moving in a circle.
In many cases the applied force will always match the right amount
Swinging a ball on a string
What happens if the ball is swung faster?

75. Just the right amount of force centripetal force

76. If too much centripetal force is applied then the object will

77. If not enough centripetal force is applied then the object will

78. As the penny spins in a circle, what is the net force on it?
For an object moving in a circle at a constant speed. The NET FORCE is the Centripetal Force.

79. When an object is swung in a vertical circle
The FNET between FG & FT supply the centripetal force FG FC

80. At the bottom of the swing, the string has to pull hardest to provide a Net force to the middle of the circle FC FC FT FG

81. At the TOP of the swing, the string pulls the least because gravity pulls toward the center.FC FC FG FT

82. Let’s say a ball on a string need 4 N of centripetal force (based on its speed). If the ball has a weight of 3 N. What is the tension in the string at the top and bottom of a vertical circle?

83. What happens to the needed centripetal force if it is swung slower?
Let’s say our 3 N ball now only needs 3 N of centripetal force
Let’s say our 3 N ball now only needs 2 N of centripetal force

84. The slowest speed an object can make a vertical loop is when the (necessary) centripetal force is equal to its weight.

85. Swinging water demo

86. If this space station is placed on earth as the highland fling, what you feel changes based on where you are in the rotation

87. Fg Fc If it is just spinning fast enough to keep you from falling off
The centripetal force needed is your weight, the floor doesn’t have to push on you at all &
You feel….. Fg Fc

88. At the bottom, the floor has to push twice as hard as your weight
And you feel…. Fc FN Fg

89. Book problems
pages

90. Book problems ?’s
Page :
10, 12, 13, 16, 17, 18, 20, 21, 22, 23, 24, 28, 29

92. Both objects have the same tangential speed but different radial distances
Which is accelerating more? (changing direction faster)
If the speed is the same the smaller the radius the more force needed

93. If an object is moving fast and makes a sharp a lot of centripetal force is needed.