Physics of Motion

8/2/2019 Physics of Motion

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Physics of Animation

Alej Garcia

Dept. PhysicsSJSU

www.algarcia.org


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Anatomy for Artists

Surgeons and artists learn anatomy, but for verydifferent purposes.

Leonardo da VinciThomas Eakins

Life drawing is difficult but its not brain surgery


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Physics for Animators

An engineers calculation of motion needs to behighly accurate, with precise measurements.

Animators, on the

other hand, usuallydont need suchmathematicalprecision. It just hasto look right.

Its not rocket science.


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Motion & Mechanics

The study of motion is a fundamental field ofphysics known as mechanics.

In order to do the fantastic we must first understand the real.

Walt Disney


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Motion & Mechanics

Physical laws apply equally to living characters,living beings are just a little more complex (butthen so is an automobile engine)

Thomas Eakins


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Physics in Maya

Animation software, such as Maya, havesophisticated physics engines that usethe laws of physics to compute motion.

Easier to use these tools knowing physics.


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Its all in the timing

An essential element of animation is the timingbetween frames

Its not

important whatgoes on eachframe of film;its the spacesbetween the

frames that areimportant. Norman McLaren


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Timing: Frames, Keys, & Clocks

Well use three different ways of measuringtime:

Frames (intervals of 1/24th of a second) Keys (given number of frames between poses) Clocks (actual seconds as measured by a clock)

IMPORTANT: Well select the keys such thatthere are always the same number of framesbetween each key.


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Uniform Motion

1 2 3 4 5

EqualDistances

NOTE: In all examples there are an equal number of frames between keys

Rolling ball is an example of uniform motion.

Velocity of the ball is constant (with no friction).

Arbitrary


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Uniform Motion in Perspective


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Uniform Motion in Perspective

Uniform motion may not appear uniform due todistortion of scale when shown in perspective.

Vanishing

Point

Horizon Line


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Accelerating Motion & Falling1

2

3

4

1

3

5

7

1

4

9

16

Falling is an example of acceleratingmotion (in animation, slowing out).

Distance between keys increases in

the ratios 1:3:5:7:9 starting frompoint of release (key #1).

Total distance from point of release

(key #1) increases in the ratios1:4:9:16:25: or 12:22:32:42:52

In Straight Ahead animation afterdrawing keys #1 and #2 the positionsof the rest are given by these rules.


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Distance FallenTime(seconds)

Frames Distance fallen(key #1 to #2)

1/24 1 1/3 inch

1/12 2 1 1/3 inches

1/8 3 3 inches

1/6 4 5 1/3 inches

6 1 foot

1/3 8 1 feet

12 4 feet2/3 16 7 feet

18 9 feet

1 24 16 feet

Distance fallen fromkey #1 (release point)to key #2 depends onthe number of framesbetween keys.

Distance fallen fromkey #2 to #3 is threetimes further; from #3to #4 is five times,from #4 to #5 is seven

times, etc.

Note: These distancedo not depend on theobjects weight.


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Falling Bowling Ball

1 (Release)

2

3

3 frames per key(and dolly in)

4

6 frames per key

4

3

2

1 (Release)

Bowling ball is onefoot in diameter.

Balls falls by onediameter in the firstsix frames.

Sametimes

5

5

Falls of diameter inthe first threeframes.


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Demo: Catch a Buck

Put thumb and index fingersnear Washingtons head. Can

you react fast enough tocatch the money?

Half length of dollar bill is 3inch so it takes about 1/8 of asecond (0.125 seconds) to fallthis distance.

Typical reaction time is 0.20 to0.25 seconds.


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Measuring Reaction Time

Release

Catch

Distance (inches) Time (sec.)1 0.072 0.103 0.12

4 0.145 0.166 0.177 0.198 0.2010 0.23

12 0.2514 0.2716 0.2918 0.30


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Rolling Downhill

13

7

1

2

3

4

Rolling downhill isalso accelerating motion

Very similar to falling except distances are smaller anddepend on the slope of the incline.

Key #1 is point of release

5


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Demo: Galileos Clicking Ramps

Roll balls down notched, inclined rampsand listen for the clicks.

Start

1 4 9 16 25 36 49 64

8 16 24 32 40 48 56 64

4=2x2 9=3x3 16=4x4 25=5x5 36=6x6 49=7x7 64=8x8


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Sliding with Friction

Sliding this way

5 3 1

1 2 3 4

Sliding with friction is another example of acceleratingmotion but in this case the object slows in.

Draw last key (where object stops) first and draw keysleading up to it in the ratios 1:3:5:7:9:

Blockstops

here


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In-betweens of Accelerated Motion

1 3 5 7

62 4

3/4 5/4 7/4 9/4 11/41/4

531

5/4+7/4 = 12/4 = 3

Accelerating this way

To draw in-betweens of accelerating motion, divide firstdistance by 4, then keep the same ratios of 1:3:5:7.

Shooting on Twos (2 frames per key)

1 frame per key


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Falling a la Chai(Extended)

1

1

3

3 4

5 7 9 11

8 8 8

Accelerating this wayReal

Falling

Fallinga la Chai

The most noticeable acceleration occurs in the initial slowing out.

Though the separations increase as an object accelerates, you canapproximate the motion as uniform for the second half of the fall.

Slowing out Uniform


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Falling and Floating

1

3

5

5

5

AcceleratingMotion

UniformMotion

Light objects, such as abeach ball, initially fall withaccelerating motion.

Due to air resistance, themotion transitions to uniformmotion after falling a certaindistance.

For very light objects, suchas a leaf, this transition is

almost immediate.

5

Squirrels cannotdie from a fall.


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Hyper-acceleration

13

7

1

2

3

4

Constant accelerationRelease

5

1

2

3

4

Release

Hyper-acceleration

If the slope of an incline increases,the acceleration itself accelerates.


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Tipping Over

A good exampleof hyper-acceleration isan objecttipping overwhen off-

balance.

No simple way to compute hyper-acceleration.

Brick tipped 2 off-balance then released.


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Acceleration Stretch

Objects do not physically stretch asthey fall (not even raindrops).

Objects visually stretchas they gain speed due tomotion blur.

Motion blur doesnot depend on theobjects material,however, it will lookmore natural forrigid objects tostretch less thanelastic objects.

High-speedcamera

Human eye


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Moving & Falling

2 3 4

5

7

3

1Arbitrary 5

1

6

7

Ball rolling off of a table combines horizontal and

vertical motion.

Falling starts with key #4, with verticaldistances increasing as 1:3:5:7:

Horizontal distances equally spaced as withuniform motion.

Arc is the combination of uniform horizontalmotion and accelerating vertical motion.


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Demo: Fall and Fire

1

5

3

1 2

3

4 4

2

3

1 FALL FIRE

One ball is releasedand falls straightdown.Other ball is fired

horizontally.At all times theballs are at thesame height.Hit the ground at

the same time.


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Parabolic Arc of Motion

2

3

4

5

7

3

15

1

6

7

Up and down motion is

symmetric, as shown.Key #4 is highest point ofthe arc of motion.

ArbitraryApex


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Bouncing

2

3

4

5

3

1 5

1

6

7

8

9

10

11

3

1Simple way to do

bouncing is to copyupper part of the arc.

Bouncing ball losses energyso it doesnt bounce up to itsoriginal height.


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Bouncing with Squash & Stretch

Stretch is added where motion is the fastest.Squash is used to emphasize impact on bounce.


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Parabolic Arc in Perspective

VP

HL

Ball starts and endson the ground.

Maximum height(ball at midpoint)


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Spinning and Tumbling

2

3

4

5

7

3

15

1

6

7

A spinning object turns by

the same (arbitrary) anglebetween keys.

Spinning occurs about theobjects center of mass.

Note: If axe is about 10 long then 4 frames between keys.

General tumbling motion (e.g., throw achair) is very complicated!

Arbitrary


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12

Brick Drop

5

3

1

3

4

5

6

A brick tipping off of atable combines all theelements describedabove: Hyper acceleration asthe brick tips over. Constant accelerationin the vertical falling.

Uniform velocity in thehorizontal motion. Constant rotation asthe brick falls.


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What creates action?

Various types of physical motion are:

Uniform motion (no acceleration) Constant acceleration Hyper-acceleration (non-constant)

But why do objects accelerate?Answer: Forces!


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Newtons First Law of Motion

An object moves with constant, uniformmotion until acted on by a force.

FORCE

No force


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First Law (Full Version)

An object at rest remains at rest &

an object in motion remains

in uniform motion*,unlessa force acts on the object.

*Moving in a straight line with constant speed.

First Law is also known asprinciple of inertia.


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Demo: Tablecloth Pull

Tablecloth

FlowerVase

Yank quickly

Due to the vases inertia it remains at rest since almostno force acts on the vase if one pulls quickly & straight.


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Demo: Riding Light Rail

When a movingtrain stops, youcontinue movingforward.

When the stoppedtrain starts movingagain, you remainstationary and arethrown backwards.

In both cases, itsdue to your inertia.


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Follow-through & Inertia

Follow-through is agood example of theprinciple of inertia.

An object wont moveuntil a force acts onit so long hair trailsbehind as head turns.

Hair then remains inmotion even afterthe head stops

turning.


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Newtons Second Law (Part 1)

The greater the force on acting on an object,the greater the acceleration of that object.


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The greater the mass of an object, the less itaccelerates when acted on by the same force.

Newtons Second Law (Part 2)


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Free Fall Acceleration

Newtons Second Law explains why heavy andlight objects fall with same acceleration.

Ratio of weightto mass alwaysthe same since

weightdepends onmass.


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Demo: Drop the Sheet

A flat sheet of paper falls slowly because of airresistance.

What happens if we place it on top of a book,blocking the air from reaching it?

AirResistance

Weight

Book and sheet falltogether


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Settle, Squash & Force of Impact

The shorter the settle the greater theforce of impact (since the decelerationis large if an object stops suddenly).

Similarly, less

squash, means

a greater force

of impact.


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Demo: Bed of Nails

One may safely lay or sit on abed of nails, as long as thereare enough nails since theforce per nail is small.

Weight of 150 pounds isdistributed over 300 nails.Force per nail is lb. Need 5lb per nail to pierce skin.

The one thing you never want to

do with a bed of nails is jumpinto bed! Big decelerationmeans big force. Ouch!


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Demo: Vampire Stake

Safest when slowly moving stake placed on asoft, fleshy spot on the chest.

X XOuch!

Quick stop, BIG FORCE

Not safe if stakestrikes hard skull

Slow settle, small force


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Newtons Third Law of Motion

For every action force there is an equalreaction force in the opposite direction.


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Walking, Running & Jumping

What forces accelerate us into motion when wewalk, run, or jump?


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Forces when Walking or Jumping

For a person walking, running, or jumping, thethree main forces on the person are:

Gravity (Downward)

Support of the floor (Upward) Frictional force of the floor (Horizontal)Only these forces can accelerate the person.Gravity is constant but the force exerted by the

floor can increase in reaction to the personexerting a force on the floor.


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Back foot pushing backon the floor.

Reaction is the friction

of the floor, whichpushes your bodyforward.

If floor is frictionless

then it is impossible tomove forward.

ReactionAction

Walking Forward


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Walk Cycle Timing

ReactionAction Reaction

Action

Right foot pushesback to accelerateforward

Right foot plants,pushing forward.Reaction of flooraccelerates yourearward.


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Jumping

Jumping is done by pushingdownward on the ground(action) so the groundpushes upward on you

(reaction).How high you jump depends

on the force and on thedistance over which you

apply that force.

Can only push while in contactwith the ground so squatting

helps by increasing distance.


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Swinging Arms and Jumping

You swing your arms upward as you jump toincrease the force pushing down on the ground.

Try jumping and swinging your arms upward afteryou leave the ground; you wont jump as high.


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Dont be discouraged

This may seem complicated (and its only Part I)but its no harder than learning anatomy.

Drawing of skeletal arms by Chuck Jones (from Chuck Amock)


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Animation Books with Physics


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The Most Important Law of Motion

The art directoris always right.

Physics of Motion

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