But really, I feel like it's difficult to understand intuitively. So, I don't remember if this was asked before...but do we actually have to type something here every time? Sometimes I just don't have much to say... I would like to go over more questions involving finding the direction of a quantity such as torque using the right hand rule, because I don't know very well how to curl your hand to find these directions Can you please play Call Me Maybe by Carly Rae Jepsen!!????????? I'm rather confused on the precession. Where does it come from? This is by far the hardest thing I've ever seen on physics. When finally engineering started to make sense, Calculus and Physics had to go wrong... This seems pretty easy. What crazy problems are you going to come up with now???? Can we do the boy sitting on a stool with a spinning top and then flip it experiment? I do not see how that can actually happen in real life. Aside from a little general review everything is cool. Happiness restored! Happy Easter! Unless you don't celebrate Easter, then happy sunday! When I first started the prelecture I thought it was going to be super difficult, but it actually wasn't all that hard to understand. Discussion was really tough this week, I didnt like it one bit. I did just watch Fight Club though and it taught me that you do have to hit rock bottom if you really want to improve yourself. what do you call a bird that doesn't eat? A polynomial! Get it?! Polly-no-meal. I probably should have brought this up sooner, but why haven't you guys been uploading the discussion problem solutions anymore? I used to rely on those to study for the discussion quizzes… Your Comments Mechanics Lecture 20, Slide 1 Rube

Exams so far Mechanics Lecture 20, Slide 2 Exam 1: 80% average Exam 2: 75% average

Physics 211 Lecture 20 Today’s Concepts: A) Angular Momentum B) Precession Mechanics Lecture 20, Slide 3 RHR recap

Student on Stool There are no external torques acting on the student-stool system, so angular momentum will be conserved. Initially: L i  I i  i Finally: L f  I f  f ff IfIf LfLf ii IiIi LiLi Mechanics Lecture 20, Slide 4

Clicker Question A student sits on a freely turning stool and rotates with constant angular velocity  1. She pulls her arms in and her angular velocity increases to  2. In doing this her kinetic energy: A) Increases B) Decreases C) Stays the same ff IfIf LfLf ii IiIi LiLi Mechanics Lecture 20, Slide 5

(using L  I  ) L is conserved: I f  I i K f  K i K increases! ff IfIf LfLf ii IiIi LiLi Mechanics Lecture 20, Slide 6

Since the student has to force her arms to move toward her body, she must be doing positive work! The work/kinetic energy theorem states that this will increase the kinetic energy of the system! ff IfIf LfLf ii IiIi LiLi Mechanics Lecture 20, Slide 7

A puck slides in a circular path on a horizontal frictionless table. It is held at a constant radius by a string threaded through a frictionless hole at the center of the table. If you pull on the string such that the radius decreases by a factor of 2, by what factor does the angular velocity of the puck increase? A) 2 B) 4 C) 8 Clicker Question Mechanics Lecture 20, Slide 8

 Since the string is pulled through a hole at the center of rotation, there is no torque: Angular momentum is conserved. R Clicker Question Mechanics Lecture 20, Slide 9

We just usedto find usually 0, but not now Food for thought (not on any test) But So how do we get an  without a  ? R Mechanics Lecture 20, Slide 10

Now suppose  EXT  0 : So in this case we can have an  without an external torque ! Food for thought (not on any test) Mechanics Lecture 20, Slide 11

Mechanics Lecture 20, Slide 12

Mechanics Lecture 19, Slide 13 Lets try it

Precession The direction of this torque at the instant shown is out of the page (using the right hand rule). The magnitude of the torque about the pivot is   Mgd. The change in angular momentum at the instant shown must also be out of the page! Mechanics Lecture 20, Slide 14

Aerial View pivot  EXT Precession  dd Mechanics Lecture 20, Slide 15

Direction: The tip of L moves in the direction of . Precession In this example : Mechanics Lecture 20, Slide 16

A disk is spinning with angular velocity  on a pivoted horizontal axle as shown. Gravity acts down. In which direction does precession cause the disk to move? A) Into the page B) Out of the page C) Up D) Down CheckPoint Mechanics Lecture 20, Slide 17

Mechanics Lecture 20, Slide 18 “I feel silly, but why doesn't the top just fall straight down each time? Is there something about the spinning motion that can sustain it at an elevated angle even when only attached at a tiny pivot point?” Here's what I kept thinking about as I went through the prelecture and it accurately describes my feelings.

Clicker Question Mechanics Lecture 20, Slide 19 The torque on the gyroscope is out of the page. In which direction must the angular momentum L change? A) Out of the pageB) Into the page

A B In which direction does point to begin with (use right hand rule)? Clicker Question Mechanics Lecture 20, Slide 20

In which direction does precession cause the disk to move? A) Into the page B) Out of the page C) Up D) Down “The torque provided by gravity is going out of the page. Therefore, L must change out of the page. Since L is in the opposite direction of the axle when drawn from the pivot, precession must make the disk go into the page.” Torque is out of the page CheckPoint Mechanics Lecture 20, Slide 21

A disk is spinning with angular velocity  on a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency . If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would: A) Increase B) Decrease C) Stay the same CheckPoint Mechanics Lecture 20, Slide 22

Mechanics Lecture 20, Slide 23 A disk is spinning with angular velocity  on a pivoted horizontal axle as shown. If the mass of the disk were doubled but its radius and angular velocity were kept the same: A) The angular momentum of the disk doubles B) The torque about the pivot doubles C) Both A and B Clicker Question L  I 

Mechanics Lecture 20, Slide 24 If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease C) Stay the same “Omega equals torque over angular momentum. Increasing mass doubles both torque and angular momentum, so nothing changes.”CheckPoint

A disk is spinning with angular velocity  on a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency . If the radius of the disk were doubled but its mass and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease C) Stay the same Clicker Question Mechanics Lecture 20, Slide 25

Wheel steers rightWheel steers left (see 2:30) Practical Application: Keeps you from falling off your bike when you ride using no hands! Riding straight  Lean Left  out of page  Lean Right  into page  Wheel steers straight Riding a Bike Mechanics Lecture 20, Slide 26

Mg d Mechanics Lecture 20, Slide 27

L  using right hand rule  Mechanics Lecture 20, Slide 28