Angular Momentum and Conservation of Momentum in Physics 101: Lecture 16, Exams of Physics

Download Angular Momentum and Conservation of Momentum in Physics 101: Lecture 16 and more Exams Physics in PDF only on Docsity!

Physics 101: Lecture 16

Angular Momentum

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

Exam II

Overview

 Review

Krotation = ½ I w^2 Torque = Force that causes rotation Equilibrium  S F = 0  S t = 0

 Today

Angular Momentum L = Iw DL = 0 if S t = 0

Define Angular Momentum

Momentum Angular Momentum p = mV L = Iw conserved if SFext = 0 conserved if Stext = Vector Vector!

units: kg-m/s units: kg-m^2 /s

Right Hand Rule

 Wrap fingers of right hand around direction of

rotation, thumb gives direction of angular

momentum.

 What is direction of angular momentum for wheel

A) Up B) Down C) Left D) Right

Act: Two Disks

 First realize that there are no external torques acting on the two-disk system. Angular momentum will be conserved!

Li w MR w i

2 (^1 )

1  I  0 

w 0

z 2 1 w f

z

Lf w w MR w f

2

 I 1 1  I 2 2 

MR w i MR w f

2 2 2

1 

w  i w f 2

1

Lecture 16, Pre-flights

You are sitting on a freely rotating bar-stool with your arms stretched out and a heavy glass mug in each hand. Your friend gives you a twist and you start rotating around a vertical axis though the center of the stool. You can assume that the bearing the stool turns on is frictionless, and that there is no net external torque present once you have started spinning.

You now pull your arms and hands (and mugs) close to your body.

Lecture 16, Preflight 1

What happens to the angular momentum as you pull in your arms?

1. it increases
2. it decreases
3. it stays the same L 1 L 2

CORRECT

“Because there are no external torques present, angular momentum is conserved”

Lecture 16, Preflight 2

w 1 w 2

I 1^ I 2

L L

What happens to your angular velocity as you pull in your arms?

1. it increases
2. it decreases
3. it stays the same

CORRECT

“you decreased the I so w increases”

What about Energy Conservation?

A) Energy isn’t conserved here

B) Energy comes from weights

C) Gravitational energy is being converted to rotational kinetic energy

D) Energy comes from cookies.

E ) I have no clue….

Turning the bike wheel

A student sits on a barstool holding a bike wheel. The wheel is initially spinning CCW in the horizontal plane (as viewed from 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

CORRECT

Start w/ angular momentum L pointing up from wheel. When wheel is flipped, no more angular momentum from it pointing up, so need to spin person/stool to conserve L!

Turning the bike wheel...

 Since there is no net external torque acting on the student-stool system, angular momentum is conserved. Remenber, L has a direction as well as a magnitude!

Initially: L INI = L W,I = + 25 kg m^2 /s

Finally: L FIN = L W,F + L S

= -25 kg m^2 /s + Ls Ls = 50 kg m^2 /s

L W,F

L S

L W,I

L W,I = L W,F + L S

Act 2 Rotations

w

 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

Puck on ice

Gyroscopic Motion:

 Suppose you have a spinning gyroscope

in the configuration shown below:

 If the left support is removed, what will

happen??

w support pivot g

Gyroscopic Motion...

 Suppose you have a spinning gyroscope

in the configuration shown below:

 If the left support is removed, what will

happen?

The gyroscope does not fall down!

w

pivot

g