PHY138Y - Mechanics - Class 12 - Mon. Oct. 25, 2004

Introduction

"Here arises a puzzle that has disturbed scientists of all periods. How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality? Can human reason without experience discover by pure thinking properties of real things?"

-- Einstein

Pre-Class Quiz #5

Last Pre-Class Quiz of the quarter
Chapter 10
Due last Wednesday
Mean: 87.6

MP Problem Set #5

Here are the results of the MP Problem Set due last Friday.

What	Number PHY138 Students Answering	PHY138 Results	The Rest of the World
Colliding Balls	980	99% correct	99%
Conservation of Momentum in Inelastic ...	978	98% correct	99%
Girl on a Trampoline	967	95% correct	92%
Collision at an Angle	961	78% correct	81%
Ball Hits a Wall Elastically	958	82% correct	79%
Time to complete	NA	54 minutes	42 minutes

Representative Assembly

This week's Representative Assembly is cancelled.

Change in Curriculum

Drop §10.10 - Precessional Motion of Gyroscopes
Add §10.11 - Rolling Motion of Rigid Bodies

About the Test

You must bring to the test:

Your student card
A soft-lead pencil

You may bring to the test:

A single 8 1/2 by 11 inch sheet of paper on which you have written anything that you wish, including both sides.
A calculator without text-storage or communication capability.

The format of the test will be:

Some multiple-choice questions. These will be worth the majority of the marks on the test.
The remainder of the marks will be determined by one multi-part question. For this question, some marks will be awarded so you will be asked to show your work.
Full details on the format will be announced on Wednesday.

The remainder of this section discusses how to study for this or any PHY138 test.

You may find it useful to review the tips on Problem Solving that we discussed in Class 3.

You can also review the tips on studying Physics that we discussed in Class 5.

If you have been keeping up with the material, especially the concepts, the good news is that you are already pretty well prepared to take the test. If you have not been keeping up, there is bad news: trying to assimilate all the sometimes subtle concepts takes time, and you have only just over a week to do that.

Whether you have been keeping up or not, there are a couple of general principles which are important:

Don't let yourself start feeling rushed. Keeping your mind calm and aware is the best state for thinking and learning.
This same state allows you to do your best on the test itself.
Don't let the details obscure the underlying physical principles. The principles are what is important, and we hope that the test will reflect this.

Things that you may wish to look over in preparation for the test include:

The textbook, class summaries, any supplemental documents that I have produced.
In-Class Questions that we have used in class.
All problems from all assignments: Pre-Class Quizzes, MP Problem Sets, Written Homework Assignments.
Last year's test, available via the PHY138 home page:
- Multiple-choice questions 1 and 2 from that test are not on material from this year's curriculum. All other questions on the test are appropriate for this year.
Last year's Final Exam.
- Multiple-choice question 1 is not on material from this year's curriculum. All other Mechanics questions on the exam are appropriate for this year.

Finally, because Physics really is only about a few powerful concepts, the last-minute cram before the test is unlikely to help and in fact can actually just confuse you. Thus, I strongly recommend that:

At least one hour or so before the beginning of the test, stop studying! If the weather is nice, consider going for a walk.

Flash Animation

As part of our discussion of a rolling wheel, we used a Flash animation to illustrate the motion of a point on the edge of the wheel.

In-Class Questions

We asked the text's Quick Quiz 10.5 in class. Initially the class was fairly evenly divided between the hollow sphere and the solid sphere, with only a few thinking they were equal After some small group discussion, about 3/4 reached the correct answer: the hollow sphere has the higher kinetic energy.
We also asked this question. Initially the class didn't have much of an idea about the answer. After some small group discussion, about 40% of you chose the correct answer: 3) 1 kg, but about half of you thought the answer was 4) 2 kg.

There are at least a couple of ways to arrive at the right answer to this question:

The center of mass of the measuring stick is 0.25 m away from the axis of rotation. So is the 1kg mass. Thus for the total torque to be zero, the mass of the stick must be 1 kg.
The quarter of the meter stick to the left of the axis of rotation is exactly balanced by the quarter of the stick just to the right of the axis. Thus their torques cancel, and we need only consider the 2 pieces to the far right of the stick. Their center of mass is located 0.5 m from the axis of rotation. So if the total torque is zero, the mass of those 2 pieces must be 0.5 kg. Therefore the total mass of the stick is 1 kg.

Supplemental Topic

As an example of equilibrium, we analysed in detail the forces acting on the leg. Notes on this have been prepared in both html and pdf format. They are accessible via the buttons to the right. We did not finish our discussion based on this document; we will finish it next class.

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