Conservation of Momentum
(SU ch. 7, OM ch. 5)
Experience of rectilinear transmission of motion. La Physique Populaire, p. 69, 1891. Public Domain, PD-1923
DAY 1: Conservation of Linear Momentum
From "beginning of chapter" to "...is completely unnoticeable."
When I am first trying to get a student to relate to momentum, I simply ask, "How willing are you to stop a moving object? Give me some examples." If you think you can safely stop something, its momentum is low. If you are unwilling to stop something, its momentum is high. What is about the object that makes you unwilling to stop it? Hopefully we get to the ideas that the objects are big (mass) and fast (velocity).
With the equation,
p = mv or p = m x v,
I just want the student to see that these quantities are directly proportional. Greater mass means greater momentum. Greater velocity means greater momentum.
DAY 2: Conservation of Linear & Angular Momentum
From "For one more example..." to "...to spinning galaxies."
DAY 3: Conservation of Angular Momentum
From "You can see conservation..." to "end of chapter"
With spinning objects, I again like to take the students back to the idea of, "How willing are you to stop a spinning object?" Unlike linear momentum (p), which depends on mass and velocity, angular momentum not only depends on mass and velocity, but also on how that mass is distributed. This may not come as intuitively to a student. At this point (and in calculus based physics and college physics), students will deal with round, symmetrical, spinning objects, so we will use r, or the radius of the object, to give us an idea on how the mass is distributed. L is the typical symbol for angular momentum, and the equation for angular momentum is:
L = rmv or L = r x m x v
All the quantities are directly proportional, so, while holding the other variables constant, an increase in mass, velocity, or radius will result in an increase in angular momentum.
If you have a spinning chair and a few books, do not skip the spinning stool demo described in the book. For angular momentum to be conserved, if the radius (r) decreases, the velocity (v) must increase.
I disagree with Mr. Fleisher's example of the earth having both angular and linear momentum. While this can, to some degree, be dependent on a person's frame of reference, the one which Mr. Fleisher is writing about is the earth moving through space. In this case, the earth actually has two types of angular momentum, one due to its spinning on its axis and another due to its orbit around the sun. The earth does not move in a straight line through space but rather in an elliptical one which we will often approximate as a circle.