1. Upcoming Deadlines
Seventh Homework – Cancelled due to furloughs (Automatic 20 points of credit) Campus-wide Furlough Day Monday, October 19th (in about 10 days) (Art/Phys 123 will meet on Wed., Oct. 21st) First Term Paper Wednesday, October 14th (week from today) For full schedule, visit course website: ArtPhysics123.pbworks.com

2. Activating your Clicker
* Turn on your clicker. * Enter the number or letter that I give you for joining this class. Hit Enter/Send key. * Clicker should read PHY123SCI2 * Type in your student ID; hit Enter/Send. Clicker is now ready to use.
Hit any key to wake the clicker from sleep mode.

3. Tipping, Turning, and Spinning

4. Understanding Rotation
Rotation was mentioned in previous lectures but now we focus on the cause of rotation.
The short answer is: torque.
The complete answer also requires you understand inertia, lever arms, etc.

5. Axis of Rotation
Rotation occurs around a line called the axis of rotation.
The axel is the axis of rotation for a set of wheels.

6. Inertia Mass is a measure of inertia for linear motion.
Rotational inertia is similar concept for rotation.
Gold brick
Normal brick M m
Difficult to move
Easy to move
Wood Bat
Plastic Pee-wee Bat x x
Difficult to Rotate
Easy to Rotate

7. Rotational Inertia Rotational inertia depends on:
Total mass of the object
How the mass is distributed
The farther the object’s mass is from the axis of rotation, the larger the rotational inertia.

8. Demo: Inertia Sticks Two metal pipes of the same mass Easy to Rotate
Hard
Lead
weights
Rotate
Axis of
Rotation

9. Human Rotational Inertia
In which pose does the dancer have a larger rotational inertia?
Axis of Rotation
Pose A
Pose B
Same for A & B since mass is unchanged. A B

10. Human Rotational Inertia
Pose B has larger rotational inertia since the leg is extended, putting mass further from the axis of rotation.
Axis of Rotation A B

11. Demo: Long Legs
Long legs have greater rotational inertia than short legs so long legged animals have a slow walking stride.

12. Demo: Drop the Stick
Two meter sticks stand upright against a wall; one has a hunk of clay on the end.
Which stick will swing down and hit the floor first?
The one without the hunk of clay.
Why?
Clay increases rotational inertia, which slows the rotation.
Axis of Rotation

13. Demo: Drop the Stick
Another way to understand why the weighted stick takes longer to fall is that it’s center of gravity is higher.
The higher it is, the longer it takes for an object to fall to the ground.
X CG
X CG
Longer stick tips over more slowly
Axis of Rotation

14. Tripping and Falling
If small child trips, he hits the ground more quickly than an adult.
Can view this two ways:
*Child has small rotational inertia.
*Child’s center of gravity is initially closer to the ground.
X CG
X CG
Axis of Rotation

15. Demo: Hammer Balance
In which case is the hammer easier to balance on your finger?
Case A
Case B
The same for A & B B A
Axis of Rotation

16. Demo: Hammer Balance
In case B the rotation is slower and thus easier to balance.
In case B the rotational inertia is greater because most of the mass is far from the axis of rotation (at your fingertip). B A
X CG
X CG

17. Tightrope Walkers
Tightrope walkers carry a long pole to increase their rotational inertia, which slows their rotation when they’re off balance.
The Great Blondin Is First to Walk Across Niagara Falls (June 30, 1859)

18. Torque When a force causes a rotation, we identify this as a torque.
Torque depends on
Magnitude of Force
Direction of Force
Lever Arm
(Torque) = (Force) x (Lever Arm)

19. Lever Arm
Lever arm is the perpendicular distance from axis of rotation to the direction of the force.

20. Opening or Closing a Door
For a door the hinge is the axis of rotation.
For maximum lever arm (and maximum torque), push perpendicular to the door at the edge opposite from the hinges.
Hinge
Door

21. Pirouettes
A ballet turn done on one leg, starting with one or both legs in plié and rising onto demi-pointe (usually for men) or pointe (usually for women).
A pirouette is typically done en dehors (moving leg starts at the front or the side and moves towards the back).
Play

22. Feet together (Harder)
Torque for a Pirouette
The farther the distance between the feet, the greater the lever arm so the greater the torque for creating the rotation.
Push on
Floor
Reaction
Force
Lever
Arm
Feet apart (Easy)
Feet together (Harder)

23. Fouetté (Whipped) Turns
A turn executed with a quick thrust of the moving leg as it passes in front of or behind the supporting leg.
Done properly, the dancer returns to the same spot at the end of the turn.
Play

24. Torque for Fouetté Turns
Push off while swinging right leg
Lower heel to the floor
Lift heel and return to point
Reaction
Force
Push on
Floor
Lever
Arm
The torque first creates a rotation of the arm & leg, then whole body rotates together

25. Fantasia (1940)
The most famous ballet scene in animation is The Dance of the Hours in Disney’s Fantasia.

26. Tipping and Torques
Slowing out as an object tips over is due to the torque created by the force of gravity. X
Lever Arm
As the tipping angle increases, the lever arm increases so the torque (and acceleration) increase as well.
Gravity Force

27. Slowing In and Slowing Out
If brick is moving upward…
If brick is not moving…
…then it slows in as it tips upward
…then it slows out as it tips over X X
The lever arm changes with angle so the timing of this slowing in or slowing out has a lot of texture.

28. Lowering the Center of Gravity
If nothing prevents a stationary object from lowering its center of gravity then it will do so.
Stepping off of a high tree branch, Tarzan swings downward on a vine. The motion may continue past the lowest point, due to follow-through (inertia), but if he keeps swinging back and forth he’ll eventually come to rest with the CG as low as possible (right under the point of suspension).

29. Tipping & Center of Gravity
A brick sitting on a ramp does not tip over if the rotation would raise the center of gravity.

30. Rolling
Wheels roll on a slope because they can always lower their center of gravity.
UNSTABLE
UNSTABLE
STABLE
Also notice the line of gravity and the base of support.

31. Class Demo: Mystery Wheel
Wheel doesn’t roll down hill. How is that possible?
Hole CG CG
Hidden
Weight
For both wheels rolling downhill would raise the center of gravity.

32. Wile E. Coyote & Tipping
Play

33. Wile E. Coyote & Tipping X
Center of Gravity ? X
Axis of Rotation
Note: This plumb line does not mark where the boulder will actually land, even if it fell to the left.
The boulder could roll to the right if the CG was far off center (vein of uranium ore?) but removing keystone unlikely to initiate that rotation.

34. Class Demo: Hammer & Hinge
How is it that the hinged board stays up?
Hinge
The center of gravity is located near the head of the hammer so the CG is lowest when the board is up.

35. Mechanical Lever
Lever converts a small force into a large force by ratio of distances acting.
Push down with a small force over a large distance
Lift a large weight over a small distance
Fulcrum
Axis of rotation goes through the fulcrum point.

36. First Class Levers
First Class Lever: Fulcrum is located in between the input force (effort) and output force (load).
Load
Arm
Effort Arm
Fulcrum
Lift a heavy load using small effort by having a long effort arm and/or short load arm.

37. Examples of First Class Levers
Trebuchet
Crowbar
Effort
Load
Fulcrum
Scissors

38. Second Class Levers
Second Class Lever: Load is located in between the effort force and the fulcrum.
Load
Arm
Effort Arm
Fulcrum
Lift a heavy load using small effort by having a long effort arm and/or short load arm.

39. Examples of Second Class Levers
Wheel Barrow
Load
Effort
Hole Punch
Fulcrum

40. Third Class Levers
Third Class Lever: Effort force is located in between the load and the fulcrum.
Load
Arm
Effort Arm
Lift a light load using large effort when the effort arm is short and/or long load arm.

41. Examples of Third Class Levers
Broom
Jaw
Fulcrum
Effort
Load

42. Human Arm as a Lever This is what type of lever? First class
Biceps muscle exerts effort force close to your elbow (fulcrum) to raise your forearm (load).
This is what type of lever?
First class
Second class
Third class

43. Human Arm as a Lever
Biceps is a third class lever so a large effort force acts over a small distance to move a small load over a large distance.
Triceps is also a third class lever, which pulls the arm in the opposite direction.
Because muscles can only contract, they’re almost always found in pairs, like biceps/triceps.

44. Human Foot as a Lever
To lift the body on the toes, the gastrocnemius (one of the strongest muscles in the body) contracts, lifting the heel upward.
Raising heel, as in walking.
Effort
Load
This is an example of a second class lever.
Fulcrum
Weight shift forward shortens the load arm, reducing the required effort by the muscle.

45. Human Neck as a Lever
The neck muscles are the body’s only first class lever and even this lever is not very efficient since the effort arm is shorter than the load arm.
Load
Fulcrum
Effort
In general, the levers in animals’ bodies sacrifice efficiency to keep a compact body form.

46. Action/Reaction for Torques
For every action force there is an equal and opposite reaction force.
The action and reaction torques, caused by these forces, might not be equal since the lever arms may be different.
However, if the action torque creates a clockwise rotation, the reaction creates a counter-clockwise rotation (and vice versa).

47. Demo: Mid-Air Twist Stand up and clear space around you.
When I say “Jump!”, jump.
In mid-air I’ll point left or right and I want you to try to turn so you land facing that direction.
Jump! Turn Land
How can you rotate in mid-air without pushing off of anything?

48. Demo: Mid-Air Twist
As you turn your legs 90 degrees, your arms and torso rotate in the opposite direction.
Sticking your arms out as you turn helps by increasing the rotational inertia of your upper body.
A large rotation of your legs is exactly cancelled by a small rotation of your outspread arms and torso.
Jump! Turn

49. Demo: Mid-Air Twist
Your rotation stops as soon as you stop rotating your upper body but by that time you’ve landed with your feet turned to the side.
Once on the ground you can push off on the ground to restore your arms and torso to a normal stance.
Turn Land

50. Front Side 180 Jump! Turn Land
The same principle is used in skateboarding tricks, such as a front side 180, in which a skater does a half turn in mid-air, turning upper and lower torso in opposite directions.

51. Demo: Drop the Cat Again

52. Demo: Drop the Cat Again
Cat lands on its feet by clever use of action/reaction combined with changing rotational inertia by extending or pulling in legs.

53. Fouetté Turns, Analyzed1 2 3 4 5 6 1 2 3 4 5 6
The torque from pushing off gives angular momentum to the right arm and leg, which rotate freely from #1 to #4.
Then the right arm and leg are made to rotate back in the opposite direction.
By action/reaction, the torso recoils and rotates in the original direction.
Play

54. Anchors Aweigh (1945)
The musical Anchors Aweigh has a famous scene in which Gene Kelley dances with Jerry the Mouse.
The scene climaxes with a series of fouetté turns. 1
@ 1:24

55. Next Lecture Squash & Stretch
First Term Paper due on Wednesday, October 14th
(In about 10 days)
Please return the clickers!

56. Simple & Complex Objects
Motion of simple objects: Position
Motion of complex objects: Position & Rotation
Axis of
Rotation
SIMPLE
COMPLEX
We’ll now examine rotation in greater detail.

57. Balance of Torques
Torques clockwise and counter-clockwise balance in both cases since
(250 N) x (3 m) = (500 N) x (1.5 m)
Her lever arm
is 3 meters

58. Supporting the Weight
To balance the weight force, the support force must be on the line of gravity.
If not, the forces create a rotating torque.
Balanced Torques CG X
Weight CG
Unbalanced Torques X
Weight
Support
Support
BASE
BASE

59. Horizontal Support
This character’s torques are balanced but in this case there is a horizontal force (support of the wall) creating the counter-torque that balances the gravity torque. X