# Lecture: Kinematics in 2 and 3 Dimensions

Don't Panic

The sites/images are mainly those of/from Wikipedia.

Sections

# Alphabetic Listing

1. Images.

2. Amazon Rainforest Images. In this catalog for river crossing problems.

3. Amazon River Images. In this catalog for river crossing problems.

4. centripetal Definition of centripetal.

5. centripetal force Images.

6. English Channel Images. It is in this catalog for channel swimming problems.

7. Galileo Images, but no parabolic motion diagrams.

8. Galileo's Analysis of Projectile Motion Images.

9. glossary of ballet Images. See the parabolic motion in le grand jete---some of us have it---and some of us don't.

10. inflection (or inflexion) point Images.

11. kinematics Images. There is a parabolic motion animation.

13. Muybridge, Eadweard (1830--1904) Images. The earliest moving pictures. The first from 1878.

14. parabola Images, but nothing great.

15. parabolic trajectory No images.

16. pi Images and animations.

17. projectile motion

Projectile motion images:

1. ParabolicWaterTrajectory.jpg So anyone who could squirt water could have seen that projectile motion was parabolic, but no until Galileo (1564--1642) knew this. You can see the parabolic arc with drinking fountains. Of course, you can't tell for sure just by looking, but anyone who tried could have figured out some way of accurately sketching the path and then some analysis would have shown that the path was a parabola. Once air drag becomes a factor, the path is no longer exactly a parabola and deviations can become quite large.
2. Grandjete.jpg---some of us have it---and some of us don't. In a grand jete, the ballerina's center of mass follows a parabola, but changing her body shape, she gives the impression of horizontal flight for an split second. When her legs lift, her center of mass moves up in her body, but that means her body tends to go lower in the air countering the rising on the parabolic arc. There is an appearance of horizontal motion for a split second.

19. trajectory Images, but nothing great. This is also what one gets for projectile motion from Wikipedia.

20. uniform circular motion Images.

# Lecture Listing 1

1. kinematics Images. There is a parabolic motion animation.

Well a lot can be said about kinematics in 2 dimensions, but in this chapter, we concentrate on projectile motion and crossing rivers, channels, etc.

Projectile motion near the Earth's surface, neglecting air resistance, has a parabolic trajectory.

The only force acting is gravity.

Short trajectories of dense objects approximate parabolic motion pretty well because air resistance has a small effect.

2. Galileo Images, but no parabolic motion diagrams.

Galileo was the first to understand this clearly---well at least to understand and tell people about it clearly.

There are some illustratons from Galileo and his contemporaries Galileo's Analysis of Projectile Motion.

You many wonder why millennia past by and no one knew this.

Without fast photography or slow motion films, it's hard see to that the motion is nearly exactly parabolic.

Even so I think people---that is early physicists---couldn't have been all that observant.

3. Muybridge, Eadweard (1830--1904) Images. The earliest moving pictures. The first from 1878.

Films came along in the 1870s, although it wasn't until the the 1890s that they took off.

Films did wonders for understanding for understanding everyday motions that were just a bit too quick for the human eye to analyze.

Well fast photography too---but fast photography implied films were possible.

Like horses galloping and buffalo running.

Old paintings of galloping horses sometimes---well maybe rarely---seem to show the horses with their feet all off the ground when the legs are spread out.

This may have been artistic licence, but it's factually incorrect and it may be that it just couldn't be figured out.

See e.g., cartoon.

Their feet are all off the ground when the legs close together.

It's hard to say who first invented film since images flicked by quickly to create a moving picture had some longish history in the 19th century, but Muybridge has a fair claim to inventing film---he was before Edison and Friese-Greene.

Muybridge also has a fair claim to inventing many film genres: the sports film---that's clearly a jockey in the galloping horse clip---and the nature film (the bison)---because of the chaste nature of this course, we won't scroll down to the first skin flick.

I still wonder if people realy weren't being all that observant.

You may not be able to see that projectile trajectories are exactly parabolic, but you can see that they approximately are.

For example in juggling: e.g., the 3-ball cascade which is slowed down; and then there is club tossing---the brothers Mitasch: world record holders.

But, of course, these are slow motion and snapshot examples.

But even so.

You can see the parabolic motion in balls rolling on inclines---which is how Galileo verified it if you allow for the facts that there are motions in 3 directions and the acceleration due to gravity is reduced by the incline and rolling effects.

5. glossary of ballet Images. See the parabolic motion in le grand jete.

Humans too can exhibit the parabolic trajectory as in le grand jete.

Of course, it is the ballerinas's center of mass that follows a parabolic arc and because they are not rigid bodies the center of mass location changes relative to their body parts.

In fact, they spread their legs wider near the top, to raise their center of mass relative to their head and shoulders---but this tends to make their head and shoulders seem to follow a more horizontal than parabolic path---and gives the impression of flying along horizonatlly.

I'd demonstrate, but some of us have it and some of us don't.

6. Amazon Rainforest Images. In this catalog for river crossing problems.

Little did you know that physics would help you during your amazing adventures crossing the Amazon River or at least one of its tributaries.

See the modest source of the Amazon---marked by a cross and a statue of an astronaut.

7. English Channel Images.

And how about that swim across the English Channel from Gris Nez (Grey Nose) to Folkestone (The peoples's stone?).

8. uniform circular motion Images.

Uniform circular motion is important in nature and technology.

In nature, it is probably most important for orbiting objects (see animation) which are often approximately in uniform circular motion---but, of course, can wildly deviate from it too.

In technology, almost all wheels make use of it at some time.