UPDATED: 6:30 PM on January 8, Solution Document Attachments Added
Cat Problem Attachment has answers on its latter pages. (You only got Page 1 of it as hard copy in class.) It references comparison to something called The Mallet Problem. If you don't have time to look at The Mallet Problem anew, that's OK. Instead, you could compare the Cat Problem to the 1993 Burning Thread Problem. But The Mallet Problem is pretty quick.
Reminders for Unit 12 Quiz:
While the quiz won't cover every single thing in the unit yet, it should have become clear through recent applications that the following skills are stressed:
1) Ability to determine moment of inertia for any object composed of the common shapes: points, rods, hoops, disks, spheres. This could be for the axis of rotation through any point in the system, so one must also know the parallel axis theorem.
2) To know the moment of inertia expression for a common shape about its center of mass, nobody must do an integral or memorize anything. The chart of common shapes' I's relative to their center of mass will be given.
3) To know how moment of inertia is applied in situations that call for Conservation of ME where K might be rotational and expressed in terms of omega.
4) To know how moment of inertia is applied in situations that call for Net Torque = (I)(alpha), and to know how lever arm is used in evaluating Torque as r X F.
5) To know how to draw perfect free body diagrams and have clear intention to use them in the process of setting up Net Torque = (I)(alpha) alongside Net Force = Ma. To know that the perfection of free body diagram drawing now requires that force vectors are located at their correct spot. Anyone who doesn't know that this last point is crucial because the location of force is what defines leverage in "Torque = r X F" is someone who is extremely far behind.
For example, no matter what I do to point this out, there always end up being people who say that gravity's torque in the burning thread problem (1993, look at it now) is MgL. This represents complete lack of physical awareness and physical definition. Actions speak louder than words: The action of writing "MgL" as gravity's torque is the same thing as shouting loudly to the world, "In that problem, I think all of the weight of the uniform rod exists just like a particle that represents ALL the mass located ONLY at the far right end of the rod." Such a notion is nonsense. It should be treated like ALL the mass located somewhere, but that somewhere is somewhere else, obviously not the right end.
6) To know how center of mass position is applied in situations that call for Conservation of ME where changes in U are still understood to be present and where the sign of U's change is to be understood.
7) The willingness and fluidity and lack of hesitation required when one needs to convert from alpha to a, omega to v, or theta to tangential distance. All of these involve radius, and one must physically understand which radius to multiply or divide by. 26% of the class passed the test on this basic piece of knowledge on January 7, 2020, and there is no Unit 12 understanding at all without it. Have fun speaking German while I speak English if you choose to remain in the 74%.
8) Be ready to continue to apply basic translational methods in the midst of a "rotational problem". There is no such thing as a "rotational problem". Be ready to apply everything learned; have a habit for setting up both translational and rotational relationships. For example, when the 1993 fake test told you to solve for the beam's acceleration of center of mass and also for the force exerted on the beam by the axis, was your habit to Diagram ALL FORCES and set up "F = Ma" as it always was supposed to have been by now? Did you do it like it was breathing? Did you then take that basic set up that's as old as October and add "a = R(alpha)" to it and add "Net Torque = (I)(alpha)" to it? If not, your eyes aren't fully open.
It would be very wise to apply the basic moment of inertia expressions and the parallel axis theorem and express the moment of inertia of the Omega-90 rod as a function of M, m, x, L, and y. It would be very wise to do this before January 9. This is because it's clearly needed for the theoretical part of the Omega-90 Experiment, and it should be obvious that doing that one is strong test prep. I'm not going to put that shape on your quiz, but the application skills in getting it are the same application skills used in whatever shape I will give you on that quiz.
It would be very wise to apply the definition of center of mass position and express the distance from system center of mass to the pivot for the Omega-90 rod as a function of M, m, x, L, and y. It would be very wise to do this before January 9. This is because it's clearly needed for the theoretical part of the Omega-90 Experiment, and it should be obvious that doing that one is strong test prep. I'm not going to put that shape on your quiz, but the application skills in getting it are the same application skills used in whatever shape I will give you on that quiz.
I'm working hard to post two more solution documents related to recent practice tests by 6 PM on Wednesday Jan. 8.
And in one of them, I'd like to close a loose end I brought up on January 7 that said, "In the Omega-90 beam, do you have to treat the point mass M like a distributed rectangle or is it safe to just treat it as a point in the moment of inertia? How safe?" You should remember me bringing this up. I then wrote the first couple terms in the total moment of inertia on the board. At the end of it, I said, "Complete the Moment of Inertia expression for the whole system. You'll need to look up the parallel axis theorem in the process. I'm hoping to include in a solution document some facts that reveal what you should have ended up writing for that.
For Omega-90, you shouldn't be waiting for my verification on whether you're getting the I correct or the center of mass position correct. You should write what you think those are and then be factoring them into the Conservation of ME theoretical solution for Omega-90. Your own measured Omega-90 is supposed to verify how you're doing. As of 1/7, 26% of Period 4 were eligible to do that, because they knew how to measure. (And everyone who did know how to measure got pretty low percent error, so this experiment is very good for teaching.)
100% of the population could know how to measure correctly. The latest attached version of the spreadsheet now assigns to everybody the R that was reported by the contest winner*. The rest of the data will be as reported by individual students on the papers I had them give me. I'll fill in the rest of the data to each individual when I get a chance.
*It's pretty interesting that the contest winner carried his R to 4 digits.