Classical Mechanics — Daily Schedule Term 3

Thursday, Oct. 30 — Study Chapter C11 — The derivation culminating in Eq. C11.14 is the central result showing that we can divvy up the total kinetic energy into C.o.M. K.E. and internal K.E. (which is very often, but not necessarily, rotational kinetic energy, but it can also be pulsations or any other internal motion) — Problem Set 11: 1. Re-do Problem 3 on Exam 1 where a rod was modeled as 20 equal masses, but this time compute the kinetic energy of the 20 masses as the whole rod undergoes rotation at angular velocity ω (note that my model of a rotating rod is a tad different than Moore’s model on p. 174, so don’t expect to quite agree with his answer); 2. C11B.6; 3. C11B.8; 4. C11M.7 (this one will really make you think)
Presentations:
- Grace: The integral in Problem C11D.1(b). I can help!
- Sam: Compute (using an integral) the kinetic energy of a spinning hollow ball. I can help!
- Sasha: Can you present C11D.4, which is an independent way of getting the kinetic energy of a spinning hollow ball? I can help!
- Brian: Start with the kinetic energy of a spinning hollow ball and use that result to go exactly the opposite direction of what Sasha is presenting (get the solid sphere’s kinetic energy by contemplating a bunch of nested hollow balls)

Monday, Nov. 3 — Study Chapter N1 — Problem Set 12: 1. N1M.3; 2. N1M.4; 3. N1D.2 (you can use the result of N1D.1); 4. N1R.3 (the job here is to compare the acceleration required to brake straight to a halt vs. the acceleration required to swerve without braking, and if you find one acceleration is less than the other, then you know what the driver should do)
Presentations:
- Grace: Present Exercise N1X.1 (and in addition, take a 2nd derivative to discover the object’s acceleration, including the acceleration’s components, magnitude, and direction)
- Sam: Show how Figure N1.6(b) illustrates the 1/r in N1.17
- Sasha: Show how Figure N1.6(c) illustrates the v² in N1.17
- Brian: Take derivatives of x(t)=A cos ωt and y(t)=A sin ωt like Grace did to get the results that Sam and Sasha got
Thursday, Nov. 6 — We will cover Chapter N2 — Problem Set 13 Forthcoming