Simple Nature - Light and Matter

The center of mass as an average example 15⊲ Explain how we know that the center of mass of each object isat the location shown in figure p.p / Example 15.⊲ The center of mass is a sort of average, so the height of thecenters of mass in 1 and 2 has to be midway between the twosquares, because that height is the average of the heights of thetwo squares. Example 3 is a combination of examples 1 and2, so we can find its center of mass by averaging the horizontalpositions of their centers of mass. In example 4, each squarehas been skewed a little, but just as much mass has been movedup as down, so the average vertical position of the mass hasn’tchanged. Example 5 is clearly not all that different from example4, the main difference being a slight clockwise rotation, so just asin example 4, the center of mass must be hanging in empty space,where there isn’t actually any mass. Horizontally, the center ofmass must be between the heels and toes, or else it wouldn’t bepossible to stand without tipping over.Momentum and Galilean relativity example 16The principle of Galilean relativity states that the laws of physicsare supposed to be equally valid in all inertial frames of reference.If we first calculate some momenta in one frame of referenceand find that momentum is conserved, and then rework thewhole problem in some other frame of reference that is movingwith respect to the first, the numerical values of the momenta willall be different. Even so, momentum will still be conserved. Allthat matters is that we work a single problem in one consistentframe of reference.One way of proving this is to apply the equation p total = m total v cm .If the velocity of one frame relative to the other is u, then the onlyeffect of changing frames of reference is to change v cm from itsoriginal value to v cm + u. This adds a constant onto the momentum,which has no effect on conservation of momentum.self-check AThe 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. 922q / Self-check A.Section 3.1 Momentum In One Dimension 143