Chapter C13

Angular Momentum

C13B.1, B.2, S.2

Due Wednesday

Monday – Review and problems Tuesday lab = conservation of angular

momentum Wednesday - review Friday - Test over chapters C1-C14

Asteroid impacts (left over from chapter 12)

The asteroid we think hit the Caribbean 65 million years ago and caused the extinction of the dinosaurs.

Diameter of asteroid ~10 km Diameter of crater = 175 km Mass = 1015 kg Velocity = 20 km/sec = 20,000 m/s. K.E. = ½mv2= 2 x 1023 j An atomic bomb = 4 x 1014 j

The atmosphere does not slow the asteroid at all.

Immediately after impact the ejected material enters the hole punched in the atmosphere and the light produced is so bright it immediately ignites all material within 1000 miles.

The whole Earth is showered with vaporized rock emitting a power 5 times that of the sun (catches many other things on fire.)

Holding rotating weights

Is something conserved? Is that something Krot=½Iω ω2?

If Krot were conserved as the moment of inertia I increased, ω must decrease

When measurements are made we find

I

I0

0

I

I0

0

Angular Momentum

Angular Momentum =L= Iω Note that this is similar to linear momentum

if I is m and ω is velocity. Linear momentum = mv So the conservation of angular momentum

then becomes:

IIL o 0

Other ways to write L

vmrprL

This is called a cross or a vector product.

Cross products

sin)()( uwwumagrmag

wur

The direction of r is perpendicular to the plane containing u and w and in a direction given by the right hand rule.

Cross product

SinBABA

A

Bθ

A=20

B=35

θ = 70º

Find AxB. = 658

What is the direction of AxB?

What is the direction of BxA?

Cross product

wuq

xyyx

zxxz

yzzy

z

y

x

wuwu

wuwu

wuwu

q

q

q

Find C = A x B

C = -31i-14j+5kzyx

zyx

BBB

AAA

zyx

BA

ˆˆˆ

Put on formula sheet.

zyxB

zyxA

ˆ5ˆ4ˆ

ˆ4ˆ3ˆ2

Differences between dot and cross products of two vectors

Dot or scalar product Answer is a scalarA∙B=ABcosθ

Cross or vector productAnswer is a vector

• Vector is perpendicular to A and B

A x B=ABsinθDirection is given by the right hand

rule.

Problems due Wednesday

C13B.1, B.2, S.2 Due Wednesday