# Lecture: One-Dimensional Kinematics

Don't Panic

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

Sections

# Alphabetic Listing

1. Images.

2. cat Images. Daredevil cats suffer from the high-rise syndrome for which there is a video Why Cats Land on Their Feet.

3. Earth's gravity Images and tables.

Wik says ``gravity'' for the acceleration due to gravity or the gravitational force per unit mass.

The symbol for this scalar quantity is g and the units are m/s**2=N/kg.

The equatorial bulge and other effects give a 9.780 N/kg to 9.832 N/kg equator to pole variation at sea level.

There is also a variation with altitude (Wik: g(y)). Note Mt. Everest goes up to 8.848 km above sea level.

The standard gravity set by convention is g_0=9.80665 N/kg. It's a conventional average.

The mean spherical non-rotating Earth g=9.823 N/kg (my calculation).

In intro classes, one usually just uses g=9.8 N/kg as a fiducial or reference value.

4. free-fall Images and animations.

5. fundamental theorem of calculus Images. There is a cute animation of converging sequence of Riemann sums: it enlarges.

6. Galileo Images.

7. gravitational acceleration No images.

8. kinematics Images and animations.

9. Leaning Tower of Pisa Images.

10. kinematic equations for constant acceleration in one-dimension Images and animations.

# Lecture Listing

1. kinematics Images and animations.

Kinematics is the description of motion without reference to causes (which in intro physics are forces).

A couple of example motions are shown in the animations: rectilinear motion and parabolic trajector motion.

Both of these cases are free-fall motions: motions where gravity is the only force acting on the moving body---air resistance is turned-off

Scroll down to the two animations.

2. kinematic equations for constant acceleration in one-dimension Images and animations.

You will get very used to the kinematic equations---1, 2, 3, and 4---so get used to them.

Here 4 of them are just being flashed at out---but you'll soon know them like the back of your hand.

Actually, I believe that there are 5 kinematic equations.

3. fundamental theorem of calculus Images and animations.

The most memorable part is ``an indefinite integration can be reversed by a differentiation''---or, in other words, an indefinite integral is an antiderivative.

This may get ahead of your calculus class, but we have to do a little differentiation and integration or antidifferentiation to derive kinematic equations for constant acceleration in one-dimension.

One needs algebra which can be tricky

Differentiation is finding the slopes of curves.

Integration is finding the area under curves.

In conception, integration is a limiting process in finding the area from a converging sequence of Riemann sums.

4. Galileo Images. See also Galileo.

The one major case where constant acceleration happens in nature is free-fall near the Earth's surface when air resistance can be neglected.

Typically, air resistance can be neglected if the object is dense and the drop relatively short.

For example in Galileo's Leaning-Tower-of-Pisa experiment.

He is thought have dropped two cannon balls of different mass.

1. Leaning Tower of Pisa Images.
2. Alileo drops the balls.
3. Commercialization of the balls.
4. The video.
5. YouTube version.

Galileo probably actually did this experiment, but it was probably more of a demonstration for the onlookers than a real experiment.

The balls didn't actually hit the ground at the same time.

``Galileo's'' point was that they would do so ideally if all complicating effects were eliminated.

This ideal way of looking at things is the path of modern physics---and many other sciences.

Find the ideal, underlying laws and then understand the actual world in terms of them allowing for complicating effects and measurement uncertainties.

5. Earth's gravity Images and tables.

Wik says ``gravity'' for the acceleration due to gravity or the gravitational force per unit mass.

The symbol for this scalar quantity is g and the units are m/s**2=N/kg.

The equatorial bulge and other effects give a 9.780 N/kg to 9.832 N/kg equator to pole variation at sea level.

There is also a variation with altitude (Wik: g(y)). Note Mt. Everest goes up to 8.848 km above sea level.

The standard gravity set by convention is g_0=9.80665 N/kg. It's a conventional average.

The mean spherical non-rotating Earth g=9.823 N/kg (my calculation).

In intro classes, one usually just uses g=9.8 N/kg as a fiducial or reference value.

6. cat Images. Daredevil cats suffer from the high-rise syndrome for which there is a video Why Cats Land on Their Feet.

Air resistance saves the cats by causing them to come to a low terminal velocity.

When falling cats first right themselves into landing position. The cat righting reflex does this.

In long falls, they stretch out to increase their air resistance. This may be instinctive or because they become relaxed.

A cat tucked in has a terminal velocity of about 27 m/s and spread out of 19 m/s (HRW-105).

This is the theory anyway.

There seems to be some question about it.

Controled experiments are needed.

The cats appearing in the video (made at the Institute of Cat Physics) gave their informed consent.

What is terminal velocity you say?

I'm glad you asked that question.

The force of air resistance increases with velocity and points opposite velocity.

Therefore air resistance increases with speed and in long falls there comes a point where air resistance practically balances gravity and the object (e.g., the cat) reaches terminal velocity.