q/Self-check A.
The center of mass as an average example 15
.Explain how we know that the center of mass of each object is
at the location shown in figure p.p/Example 15..The center of mass is a sort of average, so the height of the
centers of mass in 1 and 2 has to be midway between the two
squares, because that height is the average of the heights of the
two squares. Example 3 is a combination of examples 1 and
2, so we can find its center of mass by averaging the horizontal
positions of their centers of mass. In example 4, each square
has been skewed a little, but just as much mass has been moved
up as down, so the average vertical position of the mass hasn’t
changed. Example 5 is clearly not all that different from example
4, the main difference being a slight clockwise rotation, so just as
in example 4, the center of mass must be hanging in empty space,
where there isn’t actually any mass. Horizontally, the center of
mass must be between the heels and toes, or else it wouldn’t be
possible to stand without tipping over.
Momentum and Galilean relativity example 16
The principle of Galilean relativity states that the laws of physics
are supposed to be equally valid in all inertial frames of refer-
ence. If we first calculate some momenta in one frame of refer-
ence and find that momentum is conserved, and then rework the
whole problem in some other frame of reference that is moving
with respect to the first, the numerical values of the momenta will
all be different. Even so, momentum will still be conserved. All
that matters is that we work a single problem in one consistent
frame of reference.
One way of proving this is to apply the equationpt ot al=mt ot alvcm.
If the velocity of one frame relative to the other isu, then the only
effect of changing frames of reference is to changevcmfrom its
original value tovcm+u. This adds a constant onto the momen-
tum, which has no effect on conservation of momentum.
self-check A
The figure shows a gymnast holding onto the inside of a big wheel.
From inside the wheel, how could he make it roll one way or the other?
.Answer, p. 1055146 Chapter 3 Conservation of Momentum