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Upcoming Deadlines
Homework #9 – Stop-motion character AnimationDue Thursday, November 10th (This Thursday)20 points (10 points if late); 20 point bonus to top 3
For full schedule, visit course website:ArtPhysics123.pbworks.com
Pick up a clicker, find the right channel, and enter Student ID
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Current Event: Asteroid 2005 YU55 Passing Earth Tonight
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
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Review QuestionWhich of the following is true when the asteroid passes Earth tonight?
A) Earth applies a bigger gravitational force on the asteroid than the asteroid applies to the EarthB) Asteroid applies a bigger gravitational force on the Earth than the Earth applies to the asteroidC) The forces are the same
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Review QuestionWhich of the following is true when the asteroid passes Earth tonight?
A) Earth accelerates more than the asteroidB) The asteroid accelerates more than the Earth C) They both accelerate the same amount
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Review QuestionWhich of the following determines the rotational inertia of an object?
A) Total mass of the objectB) How the mass is distributed in the objectC) Both A and B
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C) Rotational Inertia depends on mass and how it’s distibuted
Two metal pipes of the same mass
Rotate
Leadweights
Easyto
Rotate
Hardto
Rotate
Axis ofRotation
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Demo: Hammer Balance
BA
Axis of Rotation
In which case is the hammer easier to balance on your finger?
A)Case AB)Case BC)The same for A & B
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Demo: Hammer Balance
B) Case BIn 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).
BA
X CG
X CG
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Tripping and Falling
Axis of Rotation
X CG
X CG
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.
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Tightrope Walkers
The Great Blondin Is First to Walk Across Niagara Falls (June 30, 1859)
Tightrope walkers carry a long pole to increase their rotational inertia, which slows their rotation when they’re off balance.
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When a force causes a rotation, we identify this as a torque.
Torque depends on• Magnitude of Force• Lever Arm
(Torque) = (Force) x (Lever Arm)
Torque
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Lever ArmLever arm is the perpendicular distance from axis of rotation to the direction of the force.
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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 armis 3 meters
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Supporting the WeightTo balance the weight force, the support force
must be on the line of gravity.If not, the forces create a rotating torque.
CG
Weig
ht
BASE BASE
BalancedTorques
UnbalancedTorques
Support
X
CG
Weig
ht
Support
X
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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.
DoorHinge
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Rotational Acceleration: Applying Steady Torque
Lever Arm
Force
QuickTime™ and a decompressor
are needed to see this picture.
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Pirouettes
A pirouette is typically done en dehors (moving leg starts at the front or the side and moves towards the back).
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).
http://www.youtube.com/watch?v=694S8oNXRZM
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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 onFloor
ReactionForce
LeverArm
Feet apart(Easy)
Feet together(Harder)
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Fouetté (Whipped) Turns
Done properly, the dancer returns to the same spot at the end of the turn.
A turn executed with a quick thrust of the moving leg as it passes in front of or behind the supporting leg.
http://www.youtube.com/watch?v=TV-N0QWyeac
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Torque for Fouetté Turns
Push onFloor
ReactionForce
LeverArm
Lower heel to the floor
Push off while swinging right leg
Lift heel and return to point
The torque first creates a rotation of the arm & leg, then whole body rotates together
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Fantasia (1940)
The Dance of the Hours from Disney’s Fantasia is the most famous ballet scene in animation.
http://www.youtube.com/watch?v=0pbQdtkbCcQ
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Tipping and Torques
Slowing out as an object tips over is due to the torque created by the force of gravity.
X
LeverArm
GravityForce
As the tipping angle increases, the lever arm increases so the torque (and acceleration) increase as well.
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Slowing In and Slowing Out
X
If brick is not moving…
…then it slows out as it tips over
X
If brick is moving upward…
…then it slows in as
it tips upward
The lever arm changes with angle so the timing of this slowing in or slowing out has a lot of texture.
LeverArm
LeverArm
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Horizontal Support
This character’s center of gravity is not over her base of support.
She does not tip over backwards (counter-clockwise rotation) since the wall exerts a torque in the clockwise direction, balancing the torque due to the gravity force.
Wall force
Lever
Arm
Gravity
Lever arm
Line of Gravity
X
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Mechanical Lever
Lever converts an effort force into a load force by ratio of distances acting.
Push down with a small effort force over a large distance
Lift a large load weight over a small distance
Axis of rotation goes through the fulcrum point.
Fulcrum
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First Class Levers
Fulcrum
Effort ArmLoadArm
Lift a heavy load using small effort by having a long effort arm and/or short load arm.
First Class Lever: Fulcrum is located in between the input force (effort) and output force (load).
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Efficiency vs. Speed
EffortLoad
Fulcrum
Effort
Load
Fulcrum
Efficient but slow
Inefficient but fast
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Examples of First Class Levers
Crowbar
Scissors
Trebuchet
EffortLoad
Fulcrum
Crowbar and scissors are efficient (big load force) but slow (long effort distance).
Trebuchet inefficient (big effort force) but fast (long load distance).
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Second Class Levers
Lift a heavy load using small effort by having a long effort arm and/or short load arm.
Second Class Lever: Load is located in between the effort force and the fulcrum.
Effort Arm
LoadArm
Fulcrum
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Examples of Second Class Levers
Wheel Barrow
EffortLoad
Fulcrum
Hole Punch
Second class levers are always efficient and slow.
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Third Class Levers
Third Class Lever: Effort force is located in between the load and the fulcrum.
Effort Arm
LoadArm
Third class levers are always inefficient but fast (since load arm is longer than effort arm).
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Examples of Third Class Levers
Effort
Load
Fulcrum
BroomJaw
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Human Arm as a LeverBiceps muscle exerts effort force close to your elbow (fulcrum) to raise your forearm (load).This is what type of lever?
A)First classB)Second classC)Third class
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Human Arm as a LeverBiceps 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.
EffortLoad
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Human Foot as a Lever
Effort
Load
Fulcrum
To lift the body on the toes, the gastrocnemius (one of the strongest muscles in the body) contracts, lifting the heel upward.
This is an example of a second class lever.
Raising heel, as in walking.
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Weight Shift
Effort
Load
Fulcrum
Weight shift forward shortens the load arm, reducing the required effort to lift the heel.
Effort
Load
Fulcrum
Line of Gravity Line of
Gravity
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Human Neck as a Lever
Load
Fulcrum
In general, the levers in animals’ bodies sacrifice efficiency for speed and to keep a compact body form.
The neck muscles are the body’s only first class lever This lever is not efficient since the effort arm is shorter than the load arm. Effort
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Action/Reaction for TorquesFor every action force there is an equal and
opposite reaction force.
Similarly, the action and reaction torques, caused by these forces, are equal.
Accelerations from these torques dependon objects’ rotational inertia.
If the action torque creates a clockwise rotation, the reaction creates a counter-clockwise rotation (and vice versa).
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Action/Reaction for Torques
Weightlifter exerts an action torque on the weights, rotating them counter-clockwise.
The weights exert a clockwise reaction torque, pulling the weightlifter forward.
Action
Reaction
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Fouetté Turns, Analyzed
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.
1
2
3
4
5
6
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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.
http://www.youtube.com/watch?v=xRMGRpDCW6k
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Next LectureWaves Part I
Homework 10 (Stop Motion Character Animation)
Due Nov. 10th - this Thursday
Please turn off and return the clickers!