Simple Nature - Light and Matter

Page 174: The two graphs start off with the same amplitude, but the solid curve loses amplitudemore rapidly. For a given time, t, the quantity e −ct is apparently smaller for the solid curve,meaning that ct is greater. The solid curve has the higher value of c.Page 176: A decaying exponential never dies out to zero in any finite amount of time.Page 180: In the expressionA ==F m√m (ω 2 − ωo) 2 2 + ωoω 2 2 Q −2from page 912, substituting ω = ω o makes the first term inside the square root vanish, whichshould make the denominator pretty small, thereby producing a pretty big amplitude. In thelimit of Q = ∞, Q −2 = 0, so the second term vanishes, and ω = ω o actually produces an infiniteamplitude. For values of Q that are large but finite, we still expect to get resonance pretty closeto ω = ω o . Setting ω = ω o in the finite-Q case, the first term vanishes, we can simplify thesquare root, and the result ends up being A ∝ 1/ √ Q −2 ∝ Q. This is only an approximation,because we had to assume early on that Q was large.Page 194: F = maPage 195:Answers to Self-Checks for Chapter 4Page 256: Torques 1, 2, and 4 all have the same sign, because they are trying to twist thewrench clockwise. The sign of 3 is opposite to the signs of 1, 2, and 4. The magnitude of 3 is thegreatest, since it has a large r and the force is nearly all perpendicular to the wrench. Torques1 and 2 are the same because they have the same values of r and F ⊥ . Torque 4 is the smallest,due to its small r.Page 265: One person’s θ-t graph would simply be shifted up or down relative to the others.The derivative equals the slope of the tangent line, and this slope isn’t changed when you shiftthe graph, so both people would agree on the angular velocity.Page 267: Reversing the direction of ω also reverses the direction of motion, and this is reflectedby the relationship between the plus and minus signs. In the equation for the radial acceleration,ω is squared, so even if ω is negative, the result is positive. This makes sense because theacceleration is always inward in circular motion, never outward.Page 279: All the rotations around the x axis give ω vectors along the positive x axis (thumbpointing along positive x), and all the rotations about the y axis have ω vectors with positive ycomponents.Page 282: For example, if we take (A × B) x = A y B z − B y A z and reverse the A’s and B’s, weget (B × A) x = B y A z − A y B z , which is just the negative of the original expression.Answers to Self-Checks for Chapter 5Page 301: Solids can exert shear forces. A solid could be in an equilibrium in which the shearforces were canceling the forces due to sideways pressure gradients. For example, if I push ona brick wall, it will give by perhaps a millionth of an inch, but it will reach an equilibrium, inwhich the shear forces cancel out the effect of the pressure gradient.923