Angular Momentum and Conservation of Angular Momentum in Physics 101, Study notes of Physics

Download Angular Momentum and Conservation of Angular Momentum in Physics 101 and more Study notes Physics in PDF only on Docsity!

Physics 101: Lecture 16, Pg 1

Physics 101:

Physics 101:

Lecture 16

Lecture 16

Angular Momentum

Angular Momentum

Today’s lecture will cover Textbook Chapter 8.7-8.

Physics 101: Lecture 16, Pg 2

Overview

Overview

Review



K

rotation

= ½ I

ω

2



Torque = Force that causes rotation



Equilibrium ≈ Σ

F = 0

≈ Σ τ

= 0

Today



Angular Momentum L = I

ω



L = 0 if

Σ τ

Physics 101: Lecture 16, Pg 4

Define Angular Momentum

Define Angular Momentum

Momentum Momentum

Angular Momentum Angular Momentum

p = mV

L = I

ω

conserved if

Σ

F

ext

= 0

conserved if

Στ

ext

=

Vector

Vector!

units: kg-m/s

units: kg-m

2

/s

Physics 101: Lecture 16, Pg 5

Right Hand Rule

Right Hand Rule

Wrap fingers of right hand around direction ofrotation, thumb gives direction of angularmomentum.

What is direction of angular momentum for wheel

A) Up

B) Down

C) Left

D) Right

Physics 101: Lecture 16, Pg 7

Act: Two Disks

Act: Two Disks

First realize that there are no external torquesacting on the two-disk system.



Angular momentum will be conserved!

ω

0

z

2

1

ω

f

z

Physics 101: Lecture 16, Pg 8

Lecture 16,

Lecture 16,

Pre

Pre

flights

flights

You are sitting on a freely rotating bar-stool with your armsstretched out and a heavy glass mug in each hand. Your friendgives you a twist and you start rotating around a vertical axisthough the center of the stool. You can assume that the bearing thestool turns on is frictionless, and that there is no net external torquepresent once you have started spinning.You now pull your arms and hands (and mugs) close to your body.

Physics 101: Lecture 16, Pg 10

Lecture 16,

Lecture 16,

Preflight 1

Preflight 1

What happens to the angular momentum as you pullin your arms?1. it increases2. it decreases3. it stays the same

L

1

L

2

Physics 101: Lecture 16, Pg 11

Lecture 16,

Lecture 16,

Preflight 2

Preflight 2

ω

1

ω

2

I

2

I

1

L

L

What happens to your angular velocity as you pull inyour arms?1. it increases2. it decreases3. it stays the same

Physics 101: Lecture 16, Pg 13

What about Energy Conservation?

What about Energy Conservation?

A) Energy isn’t conserved hereB) Energy comes from weightsC) Gravitational energy is being converted to

rotational kinetic energy

D) Energy comes from cookies.E ) I have no clue….

Physics 101: Lecture 16, Pg 14

Turning the bike wheel

Turning the bike wheel

A student sits on a barstool holding a bike wheel. The wheelis initially spinning CCW in the horizontal plane (as viewedfrom above) L= 25 kg m

2

/s She now turns the bike wheel

over. What happens?A. She starts to spin CCW.B. She starts to spin CW.C. Nothing

Physics 101: Lecture 16, Pg 16

Turning the bike wheel...

Turning the bike wheel...

Since there is no net external torque acting on the student-stoolsystem, angular momentum is conserved.

L L

W,F

L L

S

L L

W,I

L L

W,I

=

LL

W,F

L L

S

Physics 101: Lecture 16, Pg 17

Act 2

Act 2

Rotations

Rotations

ω

A puck slides in a circular path on a horizontal frictionless table.It is held at a constant radius by a string threaded through africtionless hole at the center of the table. If you pull on thestring 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

Physics 101: Lecture 16, Pg 19

Gyroscopic Motion:

Gyroscopic Motion:

Suppose you have a spinning gyroscopein the configuration shown below:

If the left support is removed, what willhappen??

ω

pivot

support

g

Physics 101: Lecture 16, Pg 20

Gyroscopic Motion...

Gyroscopic Motion...

Suppose you have a spinning gyroscopein the configuration shown below:

If the left support is removed, what willhappen?



The gyroscope does not fall down!

ω

pivot

g