03 Angular Momentum.pptx

(1)

I can . . .

• compare

linear momentum

to

angular

momentum

.

• _{explain the meaning of}

_{conservation of angular}

momentum

and its application to everyday

phenomena.

• identify the relationship between

rotational

inertia

,

angular velocity

and

angular momentum

.

• _{explain why}

_{angular momentum}

_{is a vector}

quantity.

• describe what effect

torque

has on

angular

(2)

Conservation of

ANGULAR MOMENTUM

(3)

Angular Momentum

_Before

Is Clockwise

Angular Momentum

_After

Is Clockwise

(4)

(5)

(6)

Angular Momentum

_Before

= Zero

Angular Momentum

_After

= Zero

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

Angular Momentum

_Before

Is Clockwise

Angular Momentum

_After

Is Clockwise

Flip wheel ½

way around

Wheel

Person

Total

Before

-1

0 -1

After

0 -1

-1

a) Clockwise

b) Counterclockwise

(17)

In your own words, explain WHY

you begin to rotate the same direction as the

wheel originally was rotating when you now

(18)

Angular Momentum

_Before

Is Clockwise

Angular Momentum

_After

Is Clockwise

Wheel

Person

Total

Before

-1

0 -1

After

+1

-2

-1

Flip wheel ALL

the way around

-1

+

+2

=

+1

a) Clockwise

b) Counterclockwise

(19)

(20)

I can . . .

• compare

linear momentum

to

angular momentum

.

• explain the meaning of

conservation of angular

momentum

and its application to everyday

phenomena.

• identify the relationship between rotational inertia,

angular velocity

and

angular momentum

.

• explain why

angular momentum

is a vector quantity.

• describe what effect

torque

has on

angular

(21)

ROTATIONAL

ANGULAR

MOMENTUM

=

· MOMENTUM

≡

Mass

· Velocity

LINEAR

“

INERTIA

IN

MOTION

”

Angular

Velocity

Rotational

Inertia

(22)

Which quantity

INCREASED?

Which quantity

DECREASED?

Which quantity

was CONSERVED?

Angular

Velocity

Rotational

Inertia

Angular

Momentum

ROTATIONAL

MOMENTUM

≡

Mass

· Velocity

LINEAR

“

INERTIA

IN

MOTION

”

ANGULAR

MOMENTUM

(23)

http://isobe.typepad.com/photo_gallery/031229_spin2.jpg

Michelle Kwan

(24)

http://www.albertson.edu/math/GradParty2000/MerryGoRound.jpg

Hum, If I

DECREASE

Rotational

Inertia

. . .

Whoa!

Way too much

Angular

Velocity

Dude!

Angular

Momentum

is CONSERVED

ANGULAR

Rotational

Angular

MOMENTUM

≡

Inertia

· Velocity

(25)

=

(

m

r

2 )

·

4 =

(

m

(

½r

)

2 )

· ω

r

½

r

(

m

r

2 )

·

4 =

(

m

¼r

2 )

· ω

4 =

¼

· ω

4 rpm

(26)

Dr. Kent Hovind – Creation Science Evangelism

The Universe was not “matter dominated” until

several thousand years after the Big Bang

ANGULAR

Rotational

Angular

MOMENTUM

≡

Inertia

· Velocity

No Mass

No

Angular

(27)

“This DVD is copyright 2002 CSE Ministry. Permission is granted to duplicate for free distribution only.

GRAVITY!

Duh!

(28)

(29)

(30)

(31)

(32)

ANGULAR MOMENTUM

is

conserved

UNLESS

acted upon by an outside

(33)

NOT ALL

FORCES

produce

TORQUE

?

But a NET

TORQUE

always changes

(34)

(35)

(36)

0.450 m

75.0 kg

½(

m

· r

2 )

_Δ

ω

= (

F

f

· r

)·Δ

t

½(

m

· r

2 )

_Δ

ω

= (

(

μ

· F

N

)

· r

)Δ

t

½(

75.0 ·0.45

2 )25 =

(

.591·

65.0 _Δ

)

_t

·0.450)Δ

_{= 11.0 seconds}

t

How much

time

will it take

the

75.0 kg

potter’s wheel

to change its

angular

velocity

from

25 rad/s

to

zero

? The

coefficient of

friction

,

μ

, is

.591

, and the

shoe is pushing with a

force of

65.0 N.

65.0 N

(37)

(38)

(39)

(40)

(41)

(42)

(43)

Torque

CHANGES

Angular Momentum

(44)

The more

LINEAR MOMENTUM

an

object has, the more

FORCE

it takes

to change the direction.

(in a short period of time)

The more

ANGULAR MOMENTUM

an

object has, the more

TORQUE

it takes

to change the direction.

(in a short period of time)

(45)

(46)

(47)

The 1.5-ton flywheel will spin at 10,000 rpm, which gives it sufficient

energy to move the 15-ton vehicle with its load of passengers 3.5 miles by

using its 112 kW generator on the flywheel shaft. When its speed has

dropped to 5,000 rpm, the driver pulls over to a charging point, where the

generator, acting as a motor, will bring the flywheel up to full speed in 90

secs. When the driver accelerates, current is drawn from the generator on

the flywheel shaft; when he brakes, the traction motor, acting as a

generator, "recharges" the flywheel (accelerates it).

(48)

Torque

Angular

Momentum

The change in

Angular Momentum

(49)

(50)

(51)

TORQUE

Angular

Momentum

(52)

http://www.mcnews.com.au/MotorcycleRacing2001/GrandPrix500/Round9/RaceImages/Germany_Pack_600p.JPG

What are the handle bars of a motorcycle for?

For holding on! (NOT for steering!)

(53)

I have asked dozens of bicycle riders

how they turn to the left. I have never

found a single person who stated all

the facts correctly when first asked.

They almost invariably said that to

turn to the left, they turned the

handlebar to the left and as a result

made a turn to the left. But on further

questioning them, some would agree

that they first turned the handlebar a

little to the right, and then as the

machine inclined to the left, they

turned the handlebar to the left and

as a result made the circle, inclining

inward.

Wilbur Wright

(54)

(55)

(56)

(57)

(58)

TORQUE

Gravity

(59)

www.arborscientific.com

Response

Torque

(60)

(61)

(62)

Forc

_e

A component of the

force

changes the

speed

.

a component of the

force

changes

direction

.

A component of the

torque

changes the

speed

.

a component of the

torque

(63)

𝐼

=

𝑚

∙

𝑟

2 𝐿

=

𝐼

∙

𝜔

𝑣

=

𝑟

∙

𝜔

=

𝑣

𝑟

𝐿

=

𝑚

∙

𝑟

2

[

𝑣

𝑟

]

𝐿

=

𝑚

∙

𝑣

∙

𝑟

Angular

Linear

to

Angular

𝑝

=

𝑚

∙

𝑣

(64)

s

=

r

· θ

v

=

r

· ω

a

=

r

· α

L

=

r

· p

=

(65)

(66)

Linear

(with respect to pivo

t)

Before

Angular After

L =

1 /

12 (m·d

2 )

· ω

L =

m·v

· r

d

(kg·m

2 )·1

/s

kg·(m/

s)·m

p = m·v

r

L =

p

· r

L =

I

· ω

m·v

· r

=

1 /

(67)

0.050 kg

(

120 m/s

)

0.050 kg

(

-23 m/s

)

0.24 m

L

_before

= L

_after

m

· v

₁

· r

=

I

· ω

+

m

· v

₂

· r

0.25 kg

(

? m/s

)

m

· v

₁

· r

= (

m

· r

2 )

v

/

r

+

m

· v

2

· r

0.20 m

0.050

·

120

·

0.20 = (

0.25

·

0.24

2 )

v

/

0.24 +

0.05

· (-23)

·

0.20

(68)

(69)

http://en.wikipedia.org/wiki/File:Earth_precession.svg

Axial precession is the movement of the

rotational axis of an astronomical body,

whereby the axis slowly traces out a cone.

In the case of the Earth, this type of

precession is also known as the

precession of the equinoxes

or

precession

of the equator

.

The Earth goes through

one such complete processional cycle in a

period of approximately 26,000 years

,

during which the positions of stars as

measured in the equatorial coordinate

system will slowly change; the change is

actually due to the change of the

coordinates. Over this cycle the Earth's

north axial pole moves from where it is

now, within 1° of Polaris, in a circle

around the ecliptic pole, with an angular

radius of about 23.5 degrees (or

approximately 23 degrees 27 arc minutes

[2]

_{). The shift is 1 degree in 72 years,}

where the angle is taken from the

observer, not from the center of the circle.

(70)

I can . . .

• compare

linear momentum

to

angular

momentum

.

• _{explain the meaning of}

_{conservation of angular}

momentum

and its application to everyday

phenomena.

• identify the relationship between

rotational

inertia

,

angular velocity

and

angular momentum

.

• _{explain why}

_{angular momentum}

_{is a vector}

quantity.

• describe what effect

torque

has on

angular