Physics 351 — Monday, March 16, 2015

I HW8 handout fits on just two sides of one sheet of paper, soI’m hoping it really is more like 5 hours. (HW8 questionsrelated to Chapter 9 are fair game for midterm.)

I This Wednesday (3/18): quiz #6 (on HW6). NextWednesday (3/25): no quiz.

I You read Ch10 (rigid body rotation) for today. The midtermexam (3/23) will cover Ch7,8,9 (not Ch10). We’ll spend 2weeks (or more?) on Ch10, starting this Wednesday.

I I’ll continue to sprinkle some Ch9 problems into futurehomeworks, to help you to assimilate the ideas. Similarly,Ch10 problems will be spread over several weeks.

I Unless you pay the extra $10/month for insurance, I don’trecommend using your smartphone for the “spinning book”experiment in Ch10! Nevertheless, Mike and Adam captured agreat slow-motion video of a tumbling iPhone, after initialrotation about e2, which I’ll show you Weds. or Fri.

If you want to see David Morin’s write-up (2 or 3 pages) of theCoriolis examples we did in class on Friday before break:

positron.hep.upenn.edu/p351/files/0306_morin_coriolis.pdf

Also, for the Lagrangian-based derivation of the pseudo-forceterms that we didn’t finish in class, I typed up a nice version at:

http://positron.hep.upenn.edu/p351/files/0306_pseudoforce_lagrange.pdf

mr = F + 2mr ×Ω + m(Ω× r)×Ω +mr × Ω

HW8#2. A puck slides with speed v on frictionless ice. Thesurface is “level” in the sense that it is orthogonal to the effective(gravitational + centrifugal) g at all points. Show that the puckmoves in a circle, as seen in the earth’s rotating frame. (Assumethat v is small enough that the radius of the circle is much smallerthan the radius of the earth, so that the colatitude θ is essentiallyconstant throughout the motion.) What is the radius of the circle?What is the frequency of the motion?

HW8#4. At a polar angle θ, a projectile is fired eastward at aninclination angle α above the ground.

(a) Find the westward and southward deflections due to theCoriolis force.

(b) In terms of θ, what angle αmax yields the maximum totaldistance of deflection? [The algebra here gets messy, so just writedown an implicit equation and don’t bother solving it for α.]

(c) What is αmax when θ equals 60, 45, and (approximately) 0?What about values of θ larger than 60? [Feel free to letMathematica do this for you, though it’s not so bad once yousimplify a bit.]

(Note also that you can use Taylor’s “show-that” problem 9.26 asa check on your expressions.)

Plug 0th order expression for velocity into expression for Coriolisforce, as Taylor did on page 353.

Uhoh — time-of-flight correction is important for ∆x. See 3/18 notes.

http://positron.hep.upenn.edu/p351/files/0311_hw08_q04.nbhttp://positron.hep.upenn.edu/p351/files/0311_hw08_q04.pdf

Physics 351 — Monday, March 16, 2015

I HW8 handout fits on just two sides of one sheet of paper, soI’m hoping it really is more like 5 hours. (HW8 questionsrelated to Chapter 9 are fair game for midterm.)

I This Wednesday (3/18): quiz #6 (on HW6). NextWednesday (3/25): no quiz.

I You read Ch10 (rigid body rotation) for today. The midtermexam (3/23) will cover Ch7,8,9 (not Ch10). We’ll spend 2weeks (or more?) on Ch10, starting this Wednesday.

I I’ll continue to sprinkle some Ch9 problems into futurehomeworks, to help you to assimilate the ideas. Similarly,Ch10 problems will be spread over several weeks.