Upcoming Deadlines Homework #9 – Stop-motion character Animation Due Thursday, November 10 th (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

Current Event: Asteroid 2005 YU55 Passing Earth Tonight

Review Question Which 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 Earth B)Asteroid applies a bigger gravitational force on the Earth than the Earth applies to the asteroid C)The forces are the same

Review Question Which of the following is true when the asteroid passes Earth tonight? A)Earth accelerates more than the asteroid B)The asteroid accelerates more than the Earth C)They both accelerate the same amount

Review Question Which of the following determines the rotational inertia of an object? A)Total mass of the object B)How the mass is distributed in the object C)Both A and B

C) Rotational Inertia depends on mass and how it’s distibuted Two metal pipes of the same mass Rotate Lead weights Easy to Rotate Hard to Rotate Axis of Rotation

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

Demo: Hammer Balance B) Case B 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

Tripping and Falling Axis of Rotation 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 Arm Lever 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 arm is 3 meters

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. CG Weight BASE Balanced Torques Unbalanced Torques Support X CG Weight 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. Door Hinge

Rotational Acceleration: Applying Steady Torque Lever Arm ForceForce

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).

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)

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.

Torque for Fouetté Turns Push on Floor Reaction Force Lever Arm 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.

Tipping and Torques Slowing out as an object tips over is due to the torque created by the force of gravity. X Lever Arm Gravity Force 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. Lever Arm

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 Arm Load Arm 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 Effort Load Fulcrum Effort Load Fulcrum Efficient but slow Inefficient but fast

Examples of First Class Levers Crowbar Scissors Trebuchet Effort Load 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 Load Arm Fulcrum

Examples of Second Class Levers Wheel Barrow Effort Load 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 Load Arm Third class levers are always inefficient but fast (since load arm is longer than effort arm).

Examples of Third Class Levers Effort Load Fulcrum Broom Jaw

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

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. Effort Load

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

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 Torques For 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 depend on 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 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

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.

Next Lecture Waves Part I Homework 10 (Stop Motion Character Animation) Due Nov. 10 th - this Thursday Please turn off and return the clickers!

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