Physics 101: Lecture 15, Pg 1

Physics 101: Physics 101: Lecture 15 Lecture 15 Angular MomentumAngular Momentum

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Exam 3

Physics 101: Lecture 15, Pg 2

Angular MomentumAngular Momentum

MomentumMomentum Angular MomentumAngular Momentum p = mV L = Iconserved if Fext = 0 conserved if ext =0Vector Vector!

units: kg-m/s units: kg-m2/s

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Physics 101: Lecture 15, Pg 3

Direction of Angular MomentumDirection of Angular Momentum

Right Hand Rule Wrap fingers of right hand around direction of

rotation, thumb gives direction of angular momentum.

Physics 101: Lecture 15, Pg 4

Example: Two DisksExample: Two Disks A disk of mass M and radius R rotates around the z axis

with angular velocity i. A second identical disk, initially not rotating, is dropped on top of the first. There is friction between the disks, and eventually they rotate together with angular velocity f. Find f.

i

z

f

z

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Physics 101: Lecture 15, Pg 5

Example: Merry Go RoundExample: Merry Go RoundFour students (mass 70kg) are riding on a merry-go-round (solid disk of mass = 90kg rotating with angular velocity =3 rad/s. Initially all four students are on the outer edge. Suddenly 3 of students pull themselves to within 0.25m of the center. What is the final angular velocity of the merry-go-round?

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Before

1.2m

After

.25

Physics 101: Lecture 15, Pg 6

Example: Merry Go RoundExample: Merry Go Round

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Before

1.2m

After

.25

Physics 101: Lecture 15, Pg 7

Example: Merry Go RoundExample: Merry Go RoundWhat is the centripetal acceleration felt by each of the students?

17

Before

1.2m

After

.25

Physics 101: Lecture 15, Pg 8

DemoDemoYou are sitting on a freely rotating bar-stool with your arms stretched out and a weight in each hand. Your professor 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 weights) close to your body.

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Physics 101: Lecture 15, Pg 9

DemoDemo What happens to the angular momentum as you pull in your arms? 1. it increases 2. it decreases 3. it stays the same L1 L2

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What happens to your angular velocity as you pull in your arms? 1. it increases 2. it decreases 3. it stays the same

Physics 101: Lecture 15, Pg 10

DemoDemoWhat happens to your kinetic energy as you pull in your arms? 1. it increases 2. it decreases 3. it stays the same

1 2

I2 I1

L L

K 12

2I 12

2 2

II 1

22

IL (using L = I )

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Physics 101: Lecture 15, Pg 11

Turning the bike wheelTurning the bike wheelA 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 m2/s She now turns the bike wheel over. What happens?

A. She starts to spin CCW.B. She starts to spin CW.C. Nothing

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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!

Physics 101: Lecture 15, Pg 12

Gyroscopic Motion:Gyroscopic Motion: Suppose you have a spinning gyroscope

in the configuration shown below: If the left support is removed, what will

happen??

pivotsupport

g

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Physics 101: Lecture 15, Pg 13

Gyroscopic Motion...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!

pivot

g

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Physics 101: Lecture 15, Pg 14

Gyroscopic Motion...Gyroscopic Motion... ... instead it precessesprecesses around its pivot

axis !

pivot

Bicycle wheel

Physics 101: Lecture 15, Pg 15

SummarySummary

= I

L = I Right Hand Rule gives directionIf = 0, L is conserved