PHY138Y - Mechanics - Class 8 - Wednesday October 4, 2006


"We all know that the real reason universities have students is to educate the professors. But, in order to be educated by the students, one has to put good questions to them. You try out your questions on the students. If there are questions that the students get interested in, then they start to tell you new things and keep you asking more new questions. Pretty soon you have learned a great deal."

-- John Archibald Wheeler (Physicist)

Just For Fun

Here is a cartoon about fictitious forces, especially the centrifugal force.

Today' Class

We finished our discussion of Chapter 7 by talking about §7.5 - Fictitious Forces and §7.6 - Nonuniform Circular Motion. I introduced the angular acceleration which is given the symbol alpha alpha; the textbook does not do this until §13.1. I then wrote the kinematic equations 7.35 using the angular acceleration.

I stressed the similarity of these equations to the corresponding constant linear acceleration equations 2.18 and 2.22.

We then make a good start on Chapter 8 - Newton's Third Law by going through Example 8.3. We will be extending this example next class.

Mathematics Background

We are beginning to need to know how to take the derivative of trig functions, although MAT135 doesn't get to this until the week of October 30. Here is a little Flash animation on this which we used in today's class.

The result is:

d(sin()) / d = cos()

d(cos()) / d = -sin()

In-Class Questions

Here are the questions I asked in today's class

Helium Balloon

About 80% of the class answered B: Johnny sees the balloon move towards the back. This is not correct: he sees the balloon move towards the front of the car. There are many ways to think about this problem. Here is one of them.

When the car begins to accelerate all masses tend to be pushed to the back of the car. However this tendency is proportional to the density of the object. If Johnny were holding a ball on a string it would move to the back. The air in the car would also be pushed to the back, but not as much as the ball, so the ball remains "under" the air. The balloon is less dense than the air (buoyant force!) and the denser air then "pushes" the balloon to the front of the car

Pendulum Bob

Nearly half the class answered A: the ball is directly over the point P. The other four answers were about equally represented. The correct answer to this question is C: the bob will be slightly to the South of point P. Here is a way to think about this question.

What is the motion of Toronto? In particular what is the orientation of the circle that it is moving in? You may wish to refer to the figure that is part of the question. So what is the direction of the centripetal acceleration? And if we are in this accelerating frame, what is the direction of the fictitious centrifugal force being exerted on the bob?

Pirate Tug of War

About 80% of the class got this correct. Well done! If you were in the minority who missed this, please be sure to understand why. A couple of free body diagrams of parts of the systems under consideration may help you.

Other Class Materials

Pdf version of the PowerPoint on the side screens. Theory of Intelligent Falling
Today's Journal. Theory of Intelligent Falling

Suggested Problems

previous class The arrows let you jump to the previous/next class summaries.