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Monday, January 28, 2013

Einstein's Brain was a Special One

In the most comprehensive study of Einstein's brain, it turns out he had an extraordinarily large prefrontal cortex, which is the area just behind your forehead.  In addition, he had a large, rectangular motor face that the author if the linked article has never seen before in any other brain.  No one is sure how this section helped Einstein reach the level of intuition, creativity and genius he had in his lifetime, but it remains a topic of interest even after nearly sixty years since Einstein's death in 1955.  This also demonstrates how much we still need to learn about the brain and human cognition.  It will be fascinating to learn of the discoveries that have yet to take place throughout your lifetime!  

Sunday, January 20, 2013

Moodle is Still Down - Another Site to Access Some Old AP Problems and Solutions

The ETHS server housing Moodle has been down since Thursday, and is still not fixed.  We do not have access to AP exams and solutions.  Here is another site that has EM exams up to 2002, with solutions.  After 2002, there are only mechanics exams.

For 2002 to 2012, the College Board has the  free response problems and solution keys, as well.  Check here!

I hope this helps a bit.  Many thanks to Erin R. for finding it!!

Wednesday, January 16, 2013

National Climate Assessment Report

If interested, check out the National Climate Assessment report, which is still in draft form.  There are 30 chapters on numerous aspects of U.S. interests that may be affected by climate.  This is a report being reviewed by the National Academies of Science, and will eventually be passed along to the Federal Government for consideration when making policy.  Let's hope reasonable minds will allow for the science to be a major guide in this process, rather than personal, financial, or political motivations overrun facts and evidence.

Tuesday, January 8, 2013

"Hardest" Majors? Engineering and Physics Top of List

A study of college students and how much time they report studying and preparing for their classes shows that engineering and physics students need to spend the most time.  This suggests that these two majors are among the most, if not the most, challenging.  This ultimately is a subjective sort of topic which leads to good debates among students and graduates, but it is likely to be about right.  Speaking from my own experience, engineering and physics students spent more time in their studies when I was in school, with often long problem sets, technically challenging topics that simply require a large amount of time to mentally digest, for engineers spending what may seem like endless hours trying to get projects working, and for physicists spending many hours in labs and research.  This would also be true for just about any science major.

Most majors in college are going to be challenging and require hard work, but a student will know if it is the right major for them if the work is difficult and yet fun, because if it is something one truly enjoys and wants to do as a career, it will be quite rewarding as time goes on.

Sunday, January 6, 2013

Case Where BOTH Linear AND Angular Momenta are Conserved!

We are used to collisions where either linear momentum is conserved, such as two billiard balls colliding, or just angular momentum is conserved, such as when a kid jumps and lands on a merry-go-round on a playground.  We are not used to seeing cases where BOTH types of momentum are conserved.  But this can happen!


When there are no net forces acting on a system, linear momentum is conserved for the system.
When there are no net torques acting on a system, angular momentum is conserved for the system.

This can happen for a rod lying on a sheet of ice or air table, where there is no friction and gravity does not affect the horizontal motion.  No part of the rod is nailed down, so the entire rod is free to move, and not just rotate.  If a particle comes flying in and sticks to the rod, then we would have both linear motion and rotational motion of the system!  And both momenta would be conserved.

A key thing to take away from this example is that there is a new center of mass of the system.  This is the key point in the problem since i) this is the point that will move along a straight line after the collision, and ii) it is the axis of rotation of the system after the collision!  Check out how to set this bugger up, and see if it makes sense.

How to do Conservation of Angular Momentum in Inelastic Collisions

This video goes through the setup for two examples of Inelastic collisions that involve rotations.  One is a sky diver landing on a spinning merry-go-round (disk) at some angle, and the sky diver 'sticks' to the platform.  If there is a component of the sky diver's motion that is perpendicular to the rotational motion of the disk, then the rotational motion will change.  Angular momentum is conserved for the system if there is no external torque acting on the system, which is the case here.  So we use the definition L = Iw for the disk since it is actually rotating, and L = mvrsin(angle between the line of motion and radius from axis of rotation).  Again, like torque, we are looking for the component of motion perpendicular to the radius line, since that is the component that can affect the rotation of the system.  

The second example is a particle moving linearly running into and sticking to a stick that is nailed down at its center. After the collision, the system only spins, so we have both L = Iw and L = mvrsin(angle).  See if the setups make sense.