Walter's Corner, Part Deux
Sat 2 April 2005
PS#9
We are now reaching the MOST DIFFICULT part of 8.01.
The PS this week is VERY HARD, VERY LONG, -- it's MURDER (sorry Alan)! START TO WORK ON THIS PS NOWWWWWWWWWWWWWWWWWWWWWWWWW (Saturday eve). This is NO joke!
There is NO WAY that we can go over all this in class in any depth.
We (I?) will have to make a choice!
* Angular Momentum (L) and Torques (Tau)
Torque=dL/dt and L=rxp (angular momentum of a point mass is the cross product between position vector and momentum).
It sounds simple, but it is not. No one (not YOU and not your instructors) have a well developed feeling for angular momentum. Spin angular momentum (I*omega) is an intrinsic property of an object and for that I have "some" feeling, but apart from "spin" angular momentum (which is independent of origin), L depends on "r" and thus on the origin that YOU choose. Depending on that choice, L can be positive, negative and also zero (this is also the case for torque). Thus, apart from spin angular momentum (e.g., the angular momentum of rotation of the Earth about its axis), L is NOT an intrinsic property of the object.
NOTHING in Physics is more non-intuitive than the behavior of Gyroscopes! This is NO exaggeration. ONLY if you do many problems will these difficult issues come to live!
PIVoT keywords: angular momentum, rolling motion, torque, gyroscope, yo-yo
ABSOLUTE MUSTS!!!!!!!
* Watch ALL of Lect #20 (nice demos)
* L21b Dynamics of a Spinning Rod (with demo) [18:05] !!!!!!!!!
* Watch ALLLLLLLL of Lect #24 - Gyroscopes - great demos!
* SG Conical Pendulum and Angular Momentum
This will give you insight in why angular momentum is so non-intuitive
1. SG8D.2 & 8E.4 L21b Dynamics of a Spinning Rod (with demo) [18:05]
2. YF10.39 A classic! You are on your own -- I'll help!!
3. SG10.1 (S) KEY Problem!!!
L21b Dynamics of a Spinning Rod [18:05]
4. SG8E8 (S) VERY important problem
L24a Pure Roll of Hollow & Solid Cylinders
5. SG9D6 I think this is somewhere on PIVoT but I cannot find it. SG Force, Torque and Work Accelerating a Car [09:02] may be useful.
6. YF10.24 This is a classic! We should do this in class.
7. SG10.11 (S) This is a famous Brain teaser!
WL Discusses a Yo-Yo Brain Teaser (with demo) [01:33]
It's a GREAT problem, and easy ONLY if you realize a KEY property of "pure roll". See YF page 371 Fig. 10.14. Pure roll (no slip) means that the angular velocity about the center of mass is ALSO the angular velocity ABOUT the point of contact with the table. Thus, by evaluating the torque about that point of contact, and NOT about the center of mass, the problem becomes a one-liner and very TRANSPARENT! I strongly advise you to do this at home!!!
8. YF10.98 This is a classic. This is a KEY problem and it is NOT easy!
The concepts behind it are discussed in WL Discusses a Hit Rod on Frictionless Surface - Part 2 [10:45] and L21b Dynamics of a Spinning Rod (with demo) [18:05] I plan to discuss this one in class (with demo).
9. YF10.27 Not too difficult.
10 YF10.55 Very useful problem - Not very difficult but very fundamental.
11 SG9C2 (S) Torque=dL/dt
12 SG9D1 (S) Solved on PIVoT
SG Tilted Rod on Rotating Table [07:12]
13 SG9D9 It may be on PIVoT somewhere but I can't find it. Nice problem.
14 SG9D4 (S) Gyroscope!!!! Lect #24.
15 YF10.48 Gyroscope -- Lect #24.
Good Luck!
\\/\////////@lter
Sun 27 March 2005
PS#8 - Welcome back from your Spring Break!
We are now getting into the "torque-angular-acceleration-moment of inertia" phase of the course. I URGE you to take this subject VERY seriously and to INHALE and DIGEST it to the maximum possible. As a logical follow-up, next week we will move on to (arguably) the most difficult part of the course: "angular momentum". It's KEY that you have this week's topics firmly under your belts. There are countless examples (some rather non-intuitive) of problems covering these rich subjects (many classics!).
***$$$***@@@==>>>MUSTS on PIVoT (keywords "torque", "moments of inertia")
Watch all of Lecture #19!!!!
"moments of inertia": MANY very useful short videos!
"torque": WL Discusses a Yo-Yo Brain Teaser [01:33]
L29b Atwood's Machine [07:51]
WL Discusses Unrolling a Rope Around a Disk [12:05]
The last VIDEO is MORE than "A MUST" (read my lips!).
1. SG8A1 piece of cake
2. YF9.66 piece of cake
3. SG8A2 (S) Math - very useful
4. SG8C3 (S) parallel and perpendicular axis theorems
5. YF9.78 Without consulting Table 9.2, THINK about the meaning of "moment-of-inertia". It may help you to realize that rotational KE is 0.5*I*w^2.
PIVoT WL Discusses Moment of Inertia [04:30]
6. SG8C4 (S) Very useful - you are likely to see one example on next Friday's exam
7. SG8C5 Applications of Parallel and Perpendicular axis theorem.
Worth doing in class. Watch PIVoT: "WL Discusses the Moment of Inertia of a Thin Rectangular Sheet"
8. YF9.85 IMPORTANT Problem! 9.85 can be done exclusively by using energy considerations - you have to include the rotational KE of the pulley. If you were also asked "when do certain things happen" then you have to calculate the angular acceleration of the pulley and the linear acceleration of the masses. For this, you should watch L29b Atwood's Machine [07:51]. It's not mentioned, but you may assume that the mass of the string is negligible.
9. YF9.89 Again, like 9.85 this can be done using energy conservation. If you were also asked "when do certain things happen", then you have to calculate the angular acceleration of the disks, and the linear acceleration of the "falling" weight. This is where the Atwood video would be very useful. It's not mentioned, but you may assume that the mass of the string is negligible.
10 SG8B2 Torque=rxF Cross product!
Keep in mind that the position vector "r" depends on YOUR CHOICE of the origin. If there were only ONE force, you can always choose an infinite number of origins so that the torque due to that one force is ZERO! In this problem, the "origin" is specified (the axes of rotation).
11 SG8E2 You now have to find BOTH the torque and the moment of inertia. The angular acceleration then follows: Torque=I*alpha. Torque is a vector and "alpha" is a vector; I is not.
12 YF10.7 see my comments under problem 11.
13 SG10.10 KEY PROBLEM - a Classic!. You now have to calculate the acceleration! Energy considerations are no longer sufficient. WL Discusses Unrolling a Rope Around a Disk [12:05] If you also want to know how to calculate the moment of inertia of a yo-yo, watch (under "yo-yo"): SG Yo-Yo [02:48]
Cheers,
\\/\/////////////@lter
Sun 13 March 2005
PS#7 -- It's again a veryyyyyyyyyyyyyyy long PS!
This week's MUSTS
* watch all of Lecture 15 (Momentum - Conservation of Momentum - Center of Mass)
* watch all of Lecture 16 (Elastic and Inelastic Collisions - Center of Mass Frame of Reference)
* watch all of Lecture 17 (Impulse - Rockets) with demo of the ballistic pendulum
* SG Elastic Collisions in One Dimension [18:27]
1. YF8.3 piece of cake
2. YF8.4 piece of cake
3. YF8.7
SG Collision, Impulse [03:42]
L17b Impulse and Impulse Time [07:33]
4. SG5B3 SG Elastic Collisions in One Dimension [18:27]
5. YF8.64 Inelastic Collision
In addition to the MUSTS, watch L18g [02:59]
6. SG7.13 Ballistic Pendulum - Solved on PIVoT - find it!
7. YF8.32 Head-on collision of 2 cars
Inelastic collision (1-D).
L16d
8. YF8.88 Super-elastic collision. Momentum is conserved - KE is NOT! Professor Guth mentions the Decay of 210Bi, however, this problem deals with the decay of 232Th. There must be some confusion here.
9. YF8.45 piece of cake
10. SG5C2 (S). Interesting problem - 2 skaters
11. SG5C4 WL Discusses the Center of Mass [03:18]
12. SG7.19 (H) This is a CLASSIC! I did it on PIVoT, but I can't find it. The Hint may be enough for you!
13. YF8.10
SG Collision, Impulse [03:42]
L17b Impulse and Impulse Time [07:33]
14. SG5A4 Reaction Force. F=dp/dt, and
action = -reaction (Newton's 3rd)
15. YF8.104 L17d and 17e!
\\/\///////@lter
Sat 5 March 2005
PS#6 It's VERY LONGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
START THIS WEEKEND!
MUSTS on PIVoT (keywords: potential energy, spring, conservation of mechanical energy, conservative force, gravitational potential energy).
* WL Discusses Conservative and Non-Conservative Forces [08:45]
* SG Potential Energy of a Spring [03:45]
* SG Work and Gravitational Potential Energy [04:07]
* L11d When the ONLY Force is Gravity [03:09]
* L11e What Matters is the Difference in PE [03:37]
* L11h Conservation of Mechanical Energy and a Wrecking Ball [03:17]
with SCARY DEMO!!!!!!!!!!!!!!
* L13a Potential Energy U(x) due to Gravity [06:55]
* L13b Calculating U(x) from F(x) and Vice Versa [08:06]
* L13c Equilibrium Points along U(x) [04:24]
These "MUSTS" add up to a total of only 51 minutes.
WATCH THEM ALL BEFORE you start this PS!
1. SG4D.1 (S) This is one of Professor Guth' favorite problems!
2. SG4B.3 SOLVED SG Potential Energy of a Spring [03:45].
I did this in class.
3. SG4B.2 (S) I did this in class.
4. YF7.43 Use Work-Energy Theorem - Piece of Cake.
Remember the W-E T always works (also when frictional forces are present)
5. SG4D.5 (S) Use Work-Energy Theorem - Piece of Cake.
6. YF7.74 Use Work-Energy Theorem - Not difficult, but not a PoC.
Let's do this in class.
7. SG4B.5 SOLVED SG Gravitation and Electrostatic Potential Energy [19:56]
8. SG4D.4 This is a classic!
SOLVED SG Simple Pendulum Hits a Pin [07:52]
DO NOT MISS L11h!!!!!!!!!!!!!!!
9. SG7.3 This is a classic!
SOLVED SG Sliding Down the Dome [09:34]
10. YF7.38 L13c Equilibrium Points along U(x) [04:24]
11. YF7.28 This is worked out in Example 7.13 page 262.
The work done by the force in going from A -> B
DEPENDS ON THE ROUTING - the force is non-conservative.
12. YF7.78 L13b Calculating U(x) from F(x) and Vice Versa [08:06]
13. SG4B4 (S) L13a Potential Energy U(x) due to Gravity [06:55]
14. YF7.80 You are on your own (for a change)!
Cheers!
\\*/\#///////////////@lter
Sun 27 Feb 2005
At the HEART of 8.01 this week is the very powerful "WORK-ENERGY THEOREM". It always WORKs (no pun implied) even when kinetic energy is converted to HEAT (due to friction)! Related topics are: Kinetic Energy and Power.
Here are a few ===>>> MUSTS <=== on PIVoT
The relevant keywords are: kinetic energy, work, work-energy theorem, and power.
* WL Discusses Work, a Dot Product [01:19]
* L11a "1D Work and Kinetic Energy" [07:32]
* L11b "Work Calculated in 3 Dimensions" [05:20]
* SG Lift 50 kg Bag over Distance h [04:05]
* L14c "Power" [06:26]
* L18a "Work-Energy theorem example [10:22]
Problems
1. SG4A.1 Piece of Cake
2. SG4A.2 - SOLVED on PIVoT ("kinetic energy")
SG Kinetic Energy in Projectile Motion [04:43]
3. SG4C.2 STUDY!!!
4. YF6.28 - PIVoT SG Potential Energy of a Spring [03:45]
5. SG4C.3 - SOLVED on PIVoT ("work")
SG Vector Valued Motion and Work [08:21]
6. SG4C.4 Swinging Pail. I discussed some if this already in class.
PIVoT L5h (you can find this under Lecture 5).
L5h Swinging Things Around on a String Vertically [08:41].
I demonstrate this by swinging a bucket of water over my head.
Also watch L7c (under "tension")
L7c Weight Swinging around on a String Vertically [05:43]
7. YF6.21 Kicking a soccer ball. Not difficult.
8. YF6.15 Work - Inclined planes.
L18a (under "work-energy theorem") could be of help.
9. YF6.81 SG Potential Energy of a Spring (under "spring potential energy") may be a help here [03:45].
10. YF6.70 Proton and Uranium Nucleus. You are on your own!
11. YF6.43 Light Bulbs. Not difficult.
12. YF6.46 Solar Power.
L14f Global Energy Consumption and Sources [10:32] (under "power") is very relevant here. Solar radiation is discussed numerically.
\\-/\+//////////////////
Sat 19 Feb 2005 (Revised Sun 20 Feb 2005)
Hello!!
Quiz #3
I thought Quiz #3 was a fair and very good quiz.
PS#4 Given the fact that you have Monday off, this is a very long Problem set. MAKE SURE TO START WORKING ON IT THIS LONG WEEKEND! There is NO WAY you can finish all this by Thur 3 PM if you start Tuesday -- NO WAY!!!!!
This week, we will cover:
* Frictional Forces
* Circular motion and the banking of tracks
* Conical Pendulum
* Air Drag - Terminal Velocity
Here are a few ABSOLUTELY MUSTS:
- Watch all of Lect #8 (Friction) on either PIVoT or on OCW 8.01 Fall 1999 (great demos!)
- Watch PIVoT "SG Conical Pendulum & Pendulum Demos" [11:50]. DO NOT watch the second video [05:04]. It also deals with the conical pendulum, but approaches it in a different way related to torques and angular momentum which we have not covered yet.
- Air Drag: Watch on PIVoT L12a [06:05] and L12b [04:16] under "air resistance or air drag". The same videos can be found under "terminal velocity".
You may also want to brush up on centripetal forces. Enter "centripetal force" in PIVoT and make a wise selection.
SG:6A.1 Piece of Cake (after having watched Lect #8)
You may also want to look at some of the many videos under "friction" (PIVoT).
Y&F5.114 This is a classic. I may have done it on PIVoT, I am not sure anymore. However, it is a GREAT problem. We should discuss it in class.
SG:6B.2 Great problem. I never saw it before. The solution is in the Study Guide. Make SURE you fully digest it!
Y&F5.62 Piece of cake, once you have watched Lect #8. Closely related in terms of the physics is SG 7.15. If needed watch "Normal and Frictional Forces" L8a [02:24] on PIVoT. It's the beginning of Lect #8.
SG:7.8 This is a classic! NOTICE the REVISED version on page 2 of the Problem set. I recommend you place yourself near the right end ON the moving belt, and solve the problem in YOUR (moving) frame of reference. At time "t=0" the suitcase is then placed on your belt with a speed "u" sliding AWAY from you. You have now converted the problem to an "easy" one: You are in the gym (wooden floor). Someone puts a suitcase on the floor and slides it away from you with speed "u". Alternatively, you place yourself on the far left end on the conveyor belt. Now, at "t=0" someone puts a suitcase on your belt with a speed "u" TOWARDS you. Your results and conclusions should be independent of which of the two locations (far right or far left on the belt) you choose. >>>>EXCEPT, that in the case you choose the Left end, the suitcase may bump into you before it comes to a rest on the belt (this is not possible if you choose the right end). However, in case you choose the Right end, you may fall off the belt before the suitcase comes to rest on the belt! IT'S KEY that you appreciate this!
SG:7.15 See above Y&F5.62.
Y&F5.95 Follow directions as given in the PS.
Y&F5.115 Nice problem! Good candidate to be discussed in class.
Y&F5.14 You are on your own. This is not a difficult problem.
Y&F5.105 Terminal velocity (see the MUSTS above).
Send me e-mail if/when needed!
\\/\/////@lter
Sat 12 Feb 2005
*****OpenCourseWare
The topics that we will cover this week, are covered in my 1999 lectures which can all be watched on OCW.
#6 Newton's Laws
#7 Weight - Perceived Gravity - Weightlessness - Free Fall
[Newton's Universal Law of Gravity is part of Lecture #11]
Tension
#8 Friction (we will have problems next week)
#10 Hooke's Law
Coulomb's Law is part of Lecture #1 of my 2002 8.02 Lectures. You can access both my 8.01 and my 8.02 lectures through OCW.
*****PIVoT
L refers to Lectures
SG refers to the Study Guide
WL I discuss concepts - often in more detail than I did in Lectures.
All my 8.01 lectures can also be watched on PIVoT (which should be fully operational now -- IF NOT send me e-mail!!). The advantage of PIVoT is that in selecting "Keywords", you can access PARTS of my lectures which are most relevant to your needs.
Here is an example. Under "gravitational force", you find way down on the list of videos: L11g "Newton's Law of Universal Gravitation". That is a 14 min and 27 second section of my lecture #11. The "g" indicates that there are 6 PIVoT segments (a-f) of Lecture #11 prior to 11g. However, those may not be relevant.
SG:2B.3 enter "spring force". The 1st video 2B.3 [07:06]
This video is also available via "superposition of forces".
SG:2B.6 enter "electrostatic force". The 1st video is 2B.6 [04:00]
SG:2C.1 enter "inclined plane". The 3rd video is 2C.1 [02:44]
SG:2C.2 enter "Newton's cradle" and watch L16e [01:56]
SG:2C.5 enter "tension". The 4th video [06:25], is strongly related
("pulling a tandem pair of sleds")
SG:2C.4 I think I did this problem (not 100% sure), but I cannot find it.
Let me know where it is "hidden" if you succeed
YF:4.49 Lg6 is A MUST!!!!!! Enjoy it; enter "tension"
YF:5.15 watch L29b Atwood's Machine [07:51] under "pulley" *** see note below
SG:3.15 enter "spring force". The 3rd video is 3.15 [02:40]
YF:4.22 enter "weight". Watch the first video "SG Weight and
Weightlessness" [15:20]. This is a MUST!!!
*** In the "real" Atwood's Machine, the moment of inertia of the pulley is a KEY element in the calculations, and that it what I do in Lecture 29.
YF:5.15 is the poor-man's version of the Atwood Machine. Watching L29b may confuse you as it deals with Torques and moments of Inertia which we have not covered yet.
I was unable to find a video which covers this simple case (perhaps it's hidden somewhere).
This is clearly a problem that we should cover in class. If you think of the "pulley" as a frictionless pin, and if you assume that the mass of the string can be ignored (we call that a "massless string"), then the Tension in the string MUST be the same everywhere in the string, BOTH on the left and on the right. Perhaps this helps!
I trust this was useful! Send me e-mail if/when you need help.
\\/\//////@lter
Wed 9 Feb 2005
On PIVoT there are 18 hours of video over and above my Fall 1999 8.01 lectures. On PIVoT I solve many of the problems of the Study Guide that we now use. At the time that I taped these, the numbers of the problems in the SG were different, however, the text is often identical.
For instance problem SG1.B.2.
Enter PIVoT. http://curricula2.mit.edu/pivot/ You have to register once which should NOT pose any problems. If it does, get back to me.
Click on "Keywords"
Click on "V"
Click on "vector components"
The very first video "SG Vector Analysis (Playing Frisbee)" is it! It lasts 6 minutes and 29 seconds. At the time, this problem was called 1.C.2.
I also do SG1.C.3 on PIVoT. Trying to find them takes some expertise; one and the same video may be found under different entries. I found it under "trajectory" (it's the first video).
Some videos refuse to come up. PIVoT experts are looking into this, and we hope that this will be solved shortly. As an example, I entered "vector subtraction" and tried to watch "WL Discusses Subtraction of Vectors" (this would be very useful for problems SG1.E.2 and Y&F3.39), but the video was not available.
As far as "centripetal acceleration" is concerned, I highly recommend under "satellite" the fifth video "SG Uniform Circular Motion and Centripetal Acceleration" (2:23). Of course, you will find the same video under "centripetal acceleration".
USE PIVoT!!!!!
\\/\//////@lter
Fri 4 Feb 2005
Hello 8.01-ers,
PS#2 will cover the following topics:
acceleration, dot products, motion in 2D and 3D, projectiles, uniform circular motion and more.
You may greatly benefit from watching some of my 8.01 lectures which can be viewed on OpenCourseWare. Enter Physics and then 8.01 Fall 1999
The relevant lectures that cover next week's material are: Lectures #2, #3, #4, and #5.
If you have any questions this weekend or later in the week, never hesitate to send me e-mail.
Greetings,
\\/\//////@lter
[top of page]
|
