PhySP19-SS4.2.3– This is a very important slide. It shows a graphical physics example of a derivative. Remember, Calculus is 90% algebra and 10% magic.
PhySP19-SS4.2.4– Here is part of that magic. At some point you have to agree that once the difference between two numbers is small enough (the ∆ gets small enough to turn into “lil d”. the two numbers essentially the same number (t1 = t2 = t).
PhySP19-SS4.2.5– ∆ —> lil d
PhySP19-SS4.2.6– I guess there IS an ultimate limit to “lil dt”. Since time is ∆x / v , turns out ∆x has a limit in our universe (Plank length) and velocity has a limit in our universe (speed of light (c)). It is called a Plank Time. The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the “quantum of time”, the smallest measurement of time that has any meaning, and is equal to 10^-43 seconds.
PhySP19-SS4.2.7– allowing (t1=t2=t) allows us magic of calculus to take place and the derivative is formed.
PhySP19-SS4.2.8– Power Rule will change your life.
PhySP19-SS4.2.9- . . .
PhySP19-SS4.2.10– Leibniz vs. Newton.
PhySP19-SS4.2.11– here is Leibniz method of writing second derivative.
PhySP19-SS4.2.12– Newton (dots) vs. Leibniz method for derivatives.
PhySP19-SS4.2.13– England vs. Germany
PhySP19-SS4.2.16– One of the classes started talking about “lil d(theta)” If one of the angles of the triangle goes to lil d(theta) the other two angles must become right angles. This will be an important concept when you get to circular motion calculus in AP Physics
PhySP19-SS4.2.17– So . . . it turns out that the 1st Orange is the derivative of the 2nd Orange.
PhySP19-SS4.2.18– Wouldn’t you rather use the Power Rule rather than do all that Stegosaurus tail stuff which takes 20 minutes.
PhySP19-SS4.2.19– Here we use Power Rule to quickly derive the velocity, acceleration and jerk in this quartet.
PhySP19-SS4.2.21– Problem 4.6.2
PhySP19-SS4.2.22– Desmos is free, but the other two are good as well.
PhySP19-SS4.2.23– You see? the jerk hides inside the first equation.
PhySP19-SS4.2.24– 1st derivative
PhySP19-SS4.2.32– that’s all we ended up doing on Wednesday.
PhySP19-SS4.2.34– Mr. Bowman’s rocket we launched during Thursday at lunch.
PhySP19-SS4.2.35– the spectators / timers / filmers
PhySP19-SS4.2. 36 — Madi pushed the launch button.
PhySP19-SS4.2. 37 — Altitude gunners
PhySP19-SS4.2. 38 — the parachute didn’t open!
PhySP19-SS4.2. 39 — 4.6.4 (a&b) The hidden jerk is the puppetmaster. Acceleration is the influencer of velocity, but acceleration is INFLUENCED by the jerk vector.
PhySP19-SS4.2. 40 — 4.6.4 (c,d,e) Students accidentally use the v bar equation in a pink quartet. Can’t use that equation in a quartet because it is parabolic.
PhySP19-SS4.2. 41 — 4.6.4 (c,d,e)
PhySP19-SS4.2. 42 — Doesn’t work for Pink.
PhySP19-SS4.2. 44 — 4.7 (the front)
PhySP19-SS4.2. 45 — Friday!
PhySP19-SS4.2. 46 — We talked about fighter pilot trainees and how they have to withstand the jerk (see the Facebook Group for videos)
PhySP19-SS4.2. 47 — A couple of classes started 4.7 (back)
PhySP19-SS4.2. 48 — Most forces we will be looking at are contact forces, but sometimes it is field forces that are running the show.