PHY138Y - Mechanics - Class 12 - Monday Oct. 20, 2003


In Class 11 we briefly mused about about what would happen if democracy applied to science. In such a case, we could vote on whether or not Newton's Second Law is true.

In 1897 the State House of Representatives of Indiana passed a bill that made the value of pi equal to exactly 3.2. You may learn more about this sad case of a democratic institution trying to legislate science at:

On Simulations versus Reality

The Flash animation of air track collisions, used in Problem Sets #5 and #6, had a bug! On Thursday morning, October 16, I fixed the bug. You may need to clear the cache of your browser to see the new version.

The existence of the bug illustrates an important principle. Simulations can, and often do, have bugs that give wrong results. However in the real air track experiment in the laboratory Nature generates the numbers, and Nature does not have bugs.

This is one reason why the laboratory uses real apparatus instead of computer simulations.

Curriculum Change

I have changed the curriculum for PHY138.

Quiz Results

The quizzes have been marked. A document on how to check your mark and the adjustments that were made may be accessed by clicking on the button to the right. Separate window, 103k. click for quiz results

About the Test

The final section of the Quiz Result document accessed above contains some information on how we will try to design the Test.

Today's Class

In discussing §7.2 - Impulse and Momentum, we discussed why cars have "crumple zones" to minimise the injuries in a crash. We showed two video clips.

The first clip is of an older car, without crumple zones. You may access it by clicking on the button to the right. The file size is 118k, and will appear in a separate window.

To view the clip requires that you have the QuickTime player installed on your computer. The player is available free from

click for the movie

The second clip is of a more modern car. You may access the clip by clicking on the button to the right. The file size is 441k.

To view it requires that you have the Real Media player installed on your computer. The player is available free from:

click to see the video

The clips are by the U.S. National Highway Traffic Safety Administration, and are used with permission. The original site of the clips is:

We combined §7.3 and §7.4 into a single discussion of collisions, and extended the textbook treatment a bit.

We considered a system of objects, with no external forces acting on the system. The objects exert forces on each other. The interaction between objects we will call a collision.

If the forces the objects exert on each other are conservative, then at all times the mechanical energy Emech = K + U is conserved. In this case the collisions between the objects are called elastic. Examples include the spring bumpers for air track cart collisions you looked at in the Flash animation for Problem Sets #5 and #6. Often, treating a collision as elastic is an approximation.

If the forces the objects exert on each other are not conservative, the potential energy can not even be defined. For these collisions the kinetic energy is not conserved. These types of collision are called inelastic. The collisions with velcro bumpers in the air track simulation are examples of inelastic collisions. In this case, some of the kinetic energy is converted into other forms.

For all collisions, elastic and inelastic, the vector momentum is conserved if the system is isolated.

In class we began Chapter 8 - Rotational Motion.

We began with §8.1 - Angular Speed and Angular Acceleration. In introducing radians for measuring angles, I mentioned that this is the "unit" that Nature seems to prefer. There are other preferences of Nature (or the way our minds think about nature). For example, whenever we think about circles we inevitably end up being confronted by the irrational number pi, which is approximately 3.14159... Similarly, whenever we think about population growth or decay we end up being confronted with e, whose value is approximately 2.71828... Nobody really knows why Nature prefers these numbers.

Note that the radian is not really a unit. It is defined as a distance, the arc length s, divided by another distance, the radius r, so has no unit. Nonetheless, in dimensional analysis we often treat it as a proper unit.

Throughout our discussion of Chapter 8, we will confine ourselves to two dimensional motion. Thus the fact that the angle theta, angular velocity omega and angular acceleration alpha are technically vectors can be mostly ignored. The vector representations of these quantities will be needed in the third section of PHY138; thus we introduced this representation.

We made an analogy between the right-hand rule used to determine the direction of the vector representations of the quantities of circular motion and a common wood screw such as shown to the right.

If we rotate the screw to drive it into a piece of wood, the direction of its angular velocity vector is in the direction that the screw moves as it goes into the wood.

wood screw

You may access the "Journal" from today's class by clicking on the button to the right. Separate window, 285k.

For reasons unknown, the Journal program decided to use very small pages today. I'll try to re-configure the program for Wednesday's class.

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