Physics 271: Advanced Honors Physics I

Recitations

Fall 2017

Week 1 to do: finish the in-class problems (answers will be posted Friday after the last recitation). If you discovered that you are rusty on (or never properly learned) unit conversions and/or sig figs, study the links in the Week 1 Useful Resources. Do homework 1 to hand in at Monday lecture (start working on it right away if you have not already done so).

Week 2 to do: if you have not seen it before (or even if you have), watch the short film "Frames of Reference" (links in the Useful Resources section) This post-Sputnik (1960) geeky classic is arguably the most perfect physics film ever made. To me, it's like Casablanca -- it gets better every time I watch it.

Week 3 to do: students in the Thursday 12:15 recitation should check out the rule for deciding which direction to draw the friction force which can be found in the problem solving toolbox below. Go over your notes for the motion of a string with mass on a frictionless pulley and fill in the remaining steps to find the magnitude of the acceleration of the string. If you need to refresh your memory or learn Taylor series (as used in the recitation discussion of the rope on the pulley), study Notes 1.2 and 1.3 on pp. 37-38 of KK. For a mathematical review, see the link in Useful Resources to the relevant pages (Sec 10.7 in 2nd ed) from the calculus text by Rogawski which is often used in Math 151/152/251.

KK 4.4. Treat the rocket as a projectile that's launched at a particular speed and angle from the launch point.

KK 4.7 Divide the motion into two time intervals and solve in each time interval separately using an appropriate approach.

KK 4.7 You will need to understand the motion of the center of mass (though in fact not the motions of the individual masses, though it is good more generally for you to understand those too) in the Push-Me-Pull-You in Example 4.7. A link to a video demo of the Push-Me-Pull-You is in the Useful Resources below.

KK 4.9 Take the sled's initial mass as M_0 (a notation that will reduce confusion with the function M(t))

KK 4.16 I suggest you solve this problem using the techniques from Chapter 3 (that is, don't try to use momentum, as the external forces exerted by the corner of the table on the string are not obvious).

IMPORTANT: in inelastic collisions, momentum is conserved but mechanical energy is NOT! The force exerted on object A by object B is equal and opposite to the force exerted on object B by object A (Newton's 3rd law) but the work done by object B on object A is not necessarily equal and opposite to the work done by object A on object B for nonconservative forces such as friction.

The geometry of the bug and ring problem in the HW is that the ring is lying flat on the table (x-y coordinate system). It has a hole drilled for the pivot and rotates around the pivot point: define the angle of the ring's position to be the angle made with the x axis by the vector from the pivot to the center of the ring.

Tip: for the falling stick problem in 7.14, the force applied at A is only to establish the initial condition for the falling stick -- that it is horizontal and not moving at t=0.

Tip: for the small oscillation problems 7.16 and 7.17, you can either compute the restoring torque for a small displacement OR expand the potential energy to quadratic order in the small displacement amplitude. For the small oscillation problem 7.9, you have no choice because of the friction forces -- you have to compute the restoring force for a small displacement.

In Problem 7.9, treat the bar as being infinitesimally thin.

*Most of the HW problems are best tackled by the extended Newton's law approach. First draw a diagram and identify the forces. Write the constraints (eg the rolling without slipping condition), Newton's 2nd law for the center of mass motion, and the torque equation, and solve. The problems involving collisions need to be solved using conservation laws (momentum, angular momentum, and mechanical energy -- it's up to you to recognize which quantities are conserved in each problem) -- the forces acting during the collision are too complicated, which rules out the Newton's law approach. For conservation law problems, draw detailed before and after diagrams.

*7.34 is another

*Specifically for 7.34: you are given that b<<R. This means that you are allowed to replace R - b by R and that you are allowed to use the flat surface rolling without slipping condition for the curved surface of the dish, which makes the problem quite easy. In fact, with a little more care, you can solve the problem without using approximations based on b<<R and still get a simple answer which is not the same but becomes the same in the limit b/R -> 0. If you want to try this, let me know and I'll give you any help you need.

*The optional falling plank problem is not as difficult as the book scares you into thinking. You should have no difficulty writing the equations with the extended Newton's law approach. It is true that to solve the equations, you need a small "trick" to get there quickly. If you are having trouble solving your equations, come to office hours or email them to me (ok to email a photo from your phone). I will check them and if correct, tell you the trick so you can finish the problem easily.

*The optional two rubber wheels problem is a rolling with slipping problem like 7.30 and 7.31. The angular momentum of the two-wheel system is NOT conserved -- can you see why?

Step 1: find fixed point (need not be in the body). Write vector omega using the description of the motion given in the problem.

Step 2: Find vector L. For most of the problems, I recommend finding L with respect to the center of mass (the vector omega is the same). Decompose vector omega into pieces for which the angular momentum is parallel to the angular velocity, Here's a big time-saver - in most of the problems, the next step will be to differentiate L with respect to t to get the torque, so you only need to find the component of L that depends on time -- don't waste effort working out the time-independent component.

Step 3: Compute vector dL/dt.

Step 4: Draw a force diagram showing all forces and points of application. Find the torque around the reference point you chose in step 2. Set this equal to dL/dt from step 3. Solve the equation for the unknown quantity,

Now, some comments on the specifics of the problems:

8.2. In the exact solution, the rotation of the disk by the turntable contributes a time-dependent angular momentum when the disk is tilted. Here, the statement that Capital Omega << omega_0 means that you are allowed to neglect this. So, the only time-dependent angular momentum that you need to consider comes from the omega_0 spin of the disk.

8.4. In order for us to compute the forces and torques on the system, since we haven't discussed the torque when the contact is not a point, we need to redraw the mechanism shown. Neglect w and imagine that the axle is rigidly attached to the wheel and connected to the shaft by a ball and socket arrangement that allows free rotation around the axis defined by the axle and is fixed in the other directions (stays perpendicular to the shaft and rotates with it). Then you can identify the force exerted by the shaft on the rigid body consisting of the wheel and axle.

8.6. (1) NOTE: the picture has many errors -- the labelling of b and R and the direction of omega_s, in particular, so draw your own.

(2) The coin cannot roll in a circle without static friction between the coin and the floor. Look at the motion of the cm and use Newton's 2nd law to help you find the direction and magnitude of the friction force.

(3) Assume b<<R. This allows you to make the approximation in the parentheses, and also to neglect the contribution to the angular momentum of the rotation of the coin around its diameter as it rolls (this makes it a lot easier to solve the final equation).

Aresty
Summer Science Research Program: an intensive, full-time,
on-campus research experience for Rutgers-New Brunswick rising
sophomores only

- our problem solving toolbox
- Week 1: Khan Academy on separable differential equations
- Week 1: significant
figures -- the basics

- Week 1: unit conversions -- the basics of the "chain-link" method
- Week 2: "Frames of Reference" part 1 (13.5 min) part 2 (14 min)
- Week 3: the "Gravity and Orbits" simulation Prof. Lath demonstrated in class Monday 18 Sept
- Week 3: the "Solar System" simulation lets you put up to 4 masses on the plane and choose initial velocities (try choosing initial positions and velocities to get 2 masses to circle around each other as we discussed in recitation).
- Week 3: Taylor series from the calculus text by Rogawski
- Week 3: problem solving checklist (the version for all problems, and a version with added comments for Newton's Laws problems)
- Week 4: add to the Newton's Laws problem-solving checklist: ONLY real physical forces should appear on the force diagram! NOTA BENE: "centripetal force" is NOT a physical force!
- Week 5: the Push-Me-Pull-You video demo
- Week 8: If you need a laugh (thanks to Anurag Modak for sharing this!)
- Week 8: The Mechanical Universe: a 52-part Introductory Physics Course: professionally produced with Prof. David Goodstein at Caltech (thanks to Larry Frolov for recommending this!)
- Week 8: Table of moments of inertia from HRW 10th ed
- Week 9: Reading for warm-up problems: rolling
without slipping, the
yo-yo

- Sundays 6:00 PM - 7:15 PM, Scott Hall 101
- Mondays 1:05 PM - 1:55 PM, lobby of Physics Lecture Hall
- Wednesdays 1:05 PM - 1:55 PM, lobby of Physics Lecture Hall
- Thursdays 1:10 PM - 1:55 PM, ARC 206
- Fridays 1:20 PM - 1:55 PM, SEC 212

In the first recitation, I suggested that you could use the textbook from your previous physics course as a reference to refresh your memory on basics you have learned before which we expect you to know. I did not take into account the fact that in most high school courses, you give the textbook back to the school at the end of the course. There are of course lots of resources on the internet where you can find the materials you need. However, if you would find it helpful to have a standard university-level calculus-based textbook (maybe even the same one you used) on hand for reference, I can lend you one for the duration of the course -- send me an email (kmrabe@physics.rutgers.edu) to let me know if you are interested. Depending on how many people ask, I should be able to get one to you without much difficulty.

If you have questions about the course or about the homework
problems, email me at kmrabe@physics.rutgers.edu

This page is maintained by Karin Rabe.