Ex. Why can't you get to LA by lifting straight up in a helicopter in NYC and just hovering there for a fewhours while Earth rotates underneath you?

Ex. What is wrong with the following statement?

"Earth cannot be rotating because if it was, then therewould be a huge wind because Earth's surface is rushingpast all of the stationary air."

Earth Earth Earth

NYCLA NYC LA

NYC

LA

Ex. What does each observer see for the path of an object dropped from a plane, train, boat, rocket, etc,that are moving at constant velocity v wrt the ground?

v

sees the ball

____________

____________

G sees the ball ____________

_________________because

the ball __________________

__________________________

fall vertically

follow a

curved path

shares therocket's horizontal v

observeron rocket

v

G = observeron the ground

G

Ex. What does each observer see for the path of an object fired vertically on a plane, train, boat, rocket, etc,that are moving at constant velocity v wrt the ground?

Observer on rocketsees the ball____________________________________

Observer G (on the ground) sees the ball _____________________________________because the ball ___________________________________

move straight upand then down

follow acurved path

shares thetrain's horizontal motion

v

v

relative motion: Observers measure ______________ velocities for the same object depending on theirmotion w.r.t. __________________ or _______________ each other. Every observer is in her/his own___________________, which is like their own personal__________________ or ______________________________.Ex: A ball thrown on a train car. Ignore air resistance.

The ball is moving at40 mph, wrt train

The train is moving at60 mph, wrt ground

Mr. Train's axes are____________ on the train

Mr. G sees Mr. T's axes _________but his own are _________________

different

(with respect to) relative to

reference framex-y axes coordinate system

stationary

xT

yT

movingstationary

xG

yG

vb,t = vt,g =

vb,g =

40 mph + 60 mph

Analyze using vectors:

Notice how the "t" subscript ____________

Result: Velocities are ___________________

in different _________________________

T measures speed of ball wrt train =__________

G measures speed of ball wrt ground = __________

40 mph

100 mph

vb,g = vb,t + vt,g

=

=

equation:

100 mph

differentreference frames

60 40

100

cancels

Ex: A ball thrown backwards on a train.

40 mph, wrt train

60 mph, wrt ground

T

G

vb,g =

vb,g = vb,t + vt,g

= =

vectors:

equation:

vb,t =

vt,g =

T sees the ball move ___________________________________G sees the ball move ___________________________________

backward at 40 mphforward at 20 mph

60

40 20

20 mph

-40 + 60

Ex: A jet flies at 600 mph, E, wrt the air. The air moves at 100 mph, W, wrt the ground.What is the velocity of the jet wrt the ground?

vj,a = +600 mph, E

va,g = 100 mph, W

vj,g = ?

vj,g = vj,a + va,g

=

=

vj,gva,g

vj,a

600 + (-100)

500 mph, E

EX. One car passes another:

EX. Two cars approach each other:

The relative speed between them = _______________

The relative speed between them = __________________

60 mph 50 mph

60 mph 50 mph

10 mph

110 mph

Ex. If objects are moving close to the speed of_________, this simple "addition of velocities" ____________________and a ________________________ equation must be used.

light cdoes not work.

more complicated

rocket's speed wrtEarth = 0.9 c

speed of torpedo wrt to ship = 0. 5 c

The speed of the torpedo as measured by someone onEarth will _____________________ which would be faster than the speed of light c! Instead, it is given by:

0.9c + 0.5c = ___________ = 1 + (0.9c)(0.5c) c2

Earth

NOT = 1.4 c

1.4 c

1.45 0.97 c

Ex. Light acts even more strangely. Suppose a ship has a special light (made of photons) weapon:

rocket's speed wrtEarth = 0.9 c speed of photon

wrt to ship = c

Earth

The speed of the photon as measured by someone onEarth will _____________________ which would be faster than the speed of light c! Instead, it is given by:

0.9c + c = ___________ = 1 + (0.9c)(c) c2

NOT = 1.9 c

1.9 c

1.9

c

____________ figured out all of these things in ________ in his Special Theory of Relativity, starting from 2 ideas:

1. The speed of light is ______________ in all reference frames.2. The Laws of Physics are __________________ in all reference frames.

From these, he also figured out that:A/ Mass is _____________________ to energy. and increases as its ________________________ .B/ Moving clocks run ____________________ .C/ Moving objects are ______________ in the direction of motion.

These results have been proven thousands of times, but are most easily observed when the speed of an object approaches _____ ,ie, in the limit as __________ .

1905

the same

the same

equivalentspeed increases

slowshrunken

c v c

Einstein

"The most incomprehensible thing about the world is that it is comprehensible."

"The only thing that interferes with my learning is my education."

Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."