Physics 211

Mechanics Lecture 19, Slide 1

Your Comments

Rube

I do not like using capital omega because it reminds me of resistance..And E&M is pure EVIL!!!!

Not so!

Personally, I feel like lecture is moving too fast, could we slow it down a little? Also, the formula's are great but it would be great if a less mathematical and more conceptual way to understand Angular Momentum Vector and Precession could be taught. Thanks! Today

It is incredibly hard to understand in what direction mass is acting on a gyroscope. Charlton Heston would have a hard time figuring the direction of Omega. Thanks for going old-school I love this class and everything, but why is the third midterm right after the thanksgiving break? :(. I don't want to work over the thanksgiving break. It's time to, you know, give thanks. (And sleep a ton.) "the tide abides for, tarrieth for no man…” is the precession causing me not to fall on the bicycle while I am turning left or right? kinda If precession occurs when the external torque is perpendicular to the L, then why do tops and even the earth precess around their axes Because there is a torque perp to L Dang. This stuff is getting really complicated. Everything after this gets easier

I'm pretty sure this is the earliest I will ever do an assignment. 2 days before it's due at 5:40 a.m. Personal Record achieved! Yay This is pretty weird stuff. Yes it is Could you please go over the ways to find the direction for angular momentum and precession? It is really confusing.... (the right hand rule stuff!) Yes I will Mechanics Lecture 20, Slide 2

I have posted the “grade estimator” on the Physics 211 webpage (for entertainment purposes only)


Physics 211 Lecture 20

Today’s Concepts:

RHR recap

A) Angular Momentum B) Precession


Student on Stool There are no external torques acting on the student-stool system, so angular momentum will be conserved. Initially: Li = Ii i Finally: Lf = If f

 f Ii = i I f f

i Ii

If Li

Lf


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

i Ii

If Li

Lf


“In the slide about angular momentum and kinetic energy, where did the equation relating K, L, and I come from? It just popped up out of nowhere.”

1 2 L2 K = I = 2 2I

Kf > Ki

If < Ii

L is conserved:

(using L = I)

K increases! f

i Ii

If Li

Lf


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

i Ii

If Li

Lf


Clicker Question 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

i

B) 4

C) 8

f


Clicker Question Since the string is pulled through a hole at the center of rotation, 2 R 2 there is noLtorque: Angular momentum is conserved. = I  = mR  = L = I  = m  1

1 1

1

2

2

  2

2

1 2 mR 1 = m R 2 4

2

2

1 1 = 2 4

2 = 41

R

R

i

f

2


Food for thought (not on any test) R

R

f

i

We just used

2

 ext = 0 to find 2 = 41  0

But

 = I

So how do we get an  without a  ?

dL d ( I ) dI d = I = = dt dt dt dt usually 0, I  but not now


Food for thought (not on any test)  EXT = I



dI dt

Now suppose EXT = 0:

dI I   =0 dt

 =

 dI I dt

So in this case we can have an  without an external torque!


“I am not buying the spinning top and stool example. I don't think it would actually work. Prove it!”


You’d have to keep spinning …


Precession The magnitude of the torque about the pivot is  = Mgd.

The direction of this torque at the instant shown is out of the page (using the right hand rule).

 ext

dL = dt

The change in angular momentum at the instant shown must also be out of the page!


Precession Aerial View

dL = Ltopd

 dL

dL d = Ltop = LtopW dt dt W EXT

 L (t ) d

 L (t  d t )

W=

pivot

 ext Ltop

“This actually seems to make a fair amount of sense! But what do you have to do when the precession frequency gets too big?” Mechanics Lecture 20, Slide 16

Precession  ext

dL = dt

In this example:

 ext = Mgd Ltop = I

W=

 ext Ltop

Mgd W= I

Direction: The tip of L moves in the direction of .


CheckPoint 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


“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. http://www.youtube.com/watch?v=WEtRoZ5FWNc


Clicker Question The torque on the gyroscope is out of the page. In which direction must the angular momentum L change?

A) Out of the page

B) Into the page

 ext

dL = dt


Clicker Question  In which direction does Lpoint to begin with (use right hand rule)?

 L

 L

A

B Mechanics Lecture 20, Slide 21

CheckPoint In which direction does precession cause the disk to move? A) Into the page B) Out of the page C) Up D) Down

 L

A) The torque caused by gravity is out of the page, so L has to change in the same direction. But, since L is in the opposite direction of the axel, precession has to make the disk go into the page.. B) The torque exerted by the gravity points out of the page Mechanics Lecture 20, Slide 22

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 W. 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


Clicker Question 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 L = I


CheckPoint 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

W=

 ext Ltop

A) Torque increases, so precession frequency increases. B) Moment of inertia increases so precession frequency decreases C) Mass affects both torque and angular momentum equally so it cancels out. Mechanics Lecture 20, Slide 25

Clicker Question A disk is spinning with angular velocity  on a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency W. 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

W=

 ext Ltop

C) Stay the same

Mgd = I


Riding a Bike Practical Application: Keeps you from falling off your bike when you ride using no hands! Riding straight ( = 0)

Wheel steers straight

Lean Left ( out of page)

Wheel steers left

Lean Right ( into page)

Wheel steers right

http://www.youtube.com/watch?v=cquvA_IpEsA (see 2:30) Mechanics Lecture 20, Slide 27

1 I = MR 2 2

 = 2 f

d Mg

L = I  = M gd

 W= L Mechanics Lecture 20, Slide 28

L

(using right hand rule)
