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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

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Current Event: Asteroid 2005 YU55 Passing Earth Tonight

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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

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

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

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

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

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

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.

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.

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

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

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

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

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

Rotational Acceleration: Applying Steady Torque

Lever Arm

Force

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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

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)

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

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

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

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.

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

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

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

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).

Efficiency vs. Speed

EffortLoad

Fulcrum

Effort

Load

Fulcrum

Efficient but slow

Inefficient but fast

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).

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

Examples of Second Class Levers

Wheel Barrow

EffortLoad

Fulcrum

Hole Punch

Second class levers are always efficient and slow.

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).

Examples of Third Class Levers

Effort

Load

Fulcrum

BroomJaw

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

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

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.

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

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

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).

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

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

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

Next LectureWaves Part I

Homework 10 (Stop Motion Character Animation)

Due Nov. 10th - this Thursday

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