Another Polar Vortex Site and Video: How is it Affected by Climate Change?

Here is another explanation for the cold weather we have been experiencing this winter.  This puts it in the context of 'global warming,' or as I prefer, climate change.  It is counterintuitive to think of regions of the world becoming colder while the earth is warming, but welcome to the world of complex systems, such as global climate.  Check out the article that goes along with the video.

Check Out Polar Vortex Explanation - NASA Satellite Data

Why is it SO COLD this winter?  Check out an explanation and imaging that will help understand from where the cold air is coming.  I hope it helps us understand what Nature is doing at the moment.

For Class Thursday, Jan 9

Check out the two videos on angular momentum, and take notes of the examples - you will get some practice right after viewing the videos.

http://docvphysics.blogspot.com/2014/01/how-to-apply-conservation-of-angular.html

http://docvphysics.blogspot.com/2013/01/case-where-both-linear-and-angular.html

How to Apply Conservation of Angular Momentum: Some Common Examples

Angular momentum is a fundamental quantity of Nature, and its conservation is used to understand the formation and shape of galaxies (notice the farther out a star is the slower it moves), how the planets orbit the sun, hurricanes and tornadoes, spinning gymnasts and divers and figure skaters, rotating and collapsing stars, and you sitting on rotating chairs.  Oh, keep in mind that 2 of the 4 quantum numbers you learn in chemistry are angular momenta.  This is an important quantity!

Here are a couple examples of how to apply conservation of angular momentum.  One version is like a kid crawling on a rotating playground disk, where we use the version L = Iw.  The moment of inertia changes, so the angular velocity must change. The second version is like a pinball machine, where a flap (rotating stick) makes a collision with a ball (point mass), and we need to figure out the speeds after the collision. See if the application of the conservation law makes sense for these and similar problems.

NO SCHOOL MONDAY, JAN. 6, or TUESDAY, JAN. 7; Final on Thursday

Due to the dangerous wind chills for Monday and also Tuesday, school has been canceled.  Be sure to check out a variety of videos, and I'll be in early Wednesday and during lunch periods, as always.  The final will be on Thursday.

Finals Week has been modified: Monday will be a regular day of classes, until 3:35 pm.  Finals will be on Tuesday, Wednesday and Thursday next week.  Friday is still a non-attendance day.  We can still use the Tuesday slot for review, and take the second final during the second slot next week.

Tunnel in NON-Uniform Charge Density Object, and Drop in an Electron: Huh??

In mechanics there is a classic 'what if' problem for gravity, where one asks what happens if you were to jump into a tunnel drilled through the center of the earth, all the way to the other side?  Conceptually you could guess you would fall in, accelerate, overshoot the center, and stop at the other side, and then fall back in and repeat.  This is precisely what would happen (minus air friction and the molten iron core burning you up, etc) if the earth had a uniform mass density.

Now, change this around electrostatics style.  With a uniformly, positively charged insulating sphere, drill a tunnel and drop an electron in.  What happens, and in addition, how fast will it be moving when it gets to the center?  How do we do this mathematically, so we have all the details?  Check here for the uniform charge density problem.

We want to complicate matters a bit more in this problem!  What if the insulating sphere has a NON-Uniform charge density, and you drill a tunnel? 

Check out this video to see how it works.  It is a Gauss's law problem to find the E-field inside.  Then, to find the speed, we need energy since this is a non-constant force problem.  We will find a strange E-field and force, which is not simple harmonic any more, and that from the E-field we can integrate to find the potential difference, and then find the change in potential energy (which becomes kinetic energy).  Lots of concepts involved, but a doable problem that is fun to think about!

Interesting Gauss's law Problem: Tunnel Through Insulating Sphere

In mechanics there is a classic 'what if' problem for gravity, where one asks what happens if you were to jump into a tunnel drilled through the center of the earth, all the way to the other side?  Conceptually you could guess you would fall in, accelerate, overshoot the center, and stop at the other side, and then fall back in and repeat.  This is precisely what would happen (minus air friction and the molten iron core burning you up, etc) if the earth had a uniform mass density.

Now, change this around electrostatics style.  With a uniformly, positively charged insulating sphere, drill a tunnel and drop an electron in.  What happens, and in addition, how fast will it be moving when it gets to the center?  How do we do this mathematically, so we have all the details?

Check out this video to see how it works.  It is a Gauss's law problem to find the E-field inside.  Then, to find the speed, we need energy since this is a non-constant force problem.  We will find that the motion is simple harmonic (like a spring, whose force is F = -kx), and that from the E-field we can integrate to find the potential difference, and then find the change in potential energy (which becomes kinetic energy).  Lots of concepts involved, but a doable problem that is fun to think about!

How to do Rolling AND Slipping Problems

In rotations, rolling without slipping is the phrase we always hope we see in a problem. Why is this good?  Because we have relationships between linear and rotational motion quantities, such as v = Rw for the linear and angular speeds, or a = R(alpha) for the linear and angular accelerations.  We also have the added benefit that the friction creating the torque on a rolling object is effectively a static friction, and no heat is produced.

These features no longer are true when the IS slipping.  This adds unknowns to the problem, since we no longer can connect the two motions together.  What do we do?  Well, other information must be given to solve the problem.  Perhaps the friction force is given in a rolling problem.  Or the tension is given in a yo-yo problem.  These are not normally given in no slipping problems.

The bottom line is we set the problems up exactly like we always do, with F = ma for linear motion and torque = I*alpha for rotational motion.  We just need to solve them separately, and not as a system.  This video will show two examples, so hopefully some of the fear of slippage will be taken away!  Check it out.