1. Ex. Why can't you get to LA by lifting straight up in a helicopter in NYC and just hovering there for a few hours while Earth rotates underneath you? Ex. What is wrong with the following statement? "Earth cannot be rotating because if it was, then there would be a huge wind because Earth's surface is rushing past all of the stationary air." Earth NYC LA NYC LA NYC LA

2. 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 the rocket's horizontal v observer on rocket v G = observer on the ground G

3. 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 rocket sees the ball __________________ Observer G (on the ground) sees the ball ____________ _________________________ because the ball _________ __________________________ move straight up and then down follow a curved path shares the train's horizontal motion v v

4. relative motion: Observers measure ______________ velocities for the same object depending on their motion 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 at 40 mph, wrt train The train is moving at 60 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 frame x-y axescoordinate system stationary xTxT yTyT moving stationary xGxG yGyG

5. v b,t = v t,g = v b,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 v b,g = v b,t + v t,g = equation: 100 mph different reference frames 60 40 100 cancels

6. Ex: A ball thrown backwards on a train. 40 mph, wrt train 60 mph, wrt ground T G v b,g = v b,g = v b,t + v t,g = vectors: equation: v b,t = v t,g = T sees the ball move ___________________________________ G sees the ball move ___________________________________ backward at 40 mph forward at 20 mph 60 40 20 20 mph -40 + 60

7. 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? v j,a = +600 mph, E v a,g = 100 mph, W v j,g = ? v j,g = v j,a + v a,g = v j,g v a,g v j,a 600 + (-100) 500 mph, E

8. 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

9. Ex. If objects are moving close to the speed of_________, this simple "addition of velocities" ____________________ and a ________________________ equation must be used. light c does not work. more complicated rocket's speed wrt Earth = 0.9 c speed of torpedo wrt to ship = 0. 5 c The speed of the torpedo as measured by someone on Earth 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) c 2 Earth NOT = 1.4 c 1.4 c 1.45 0.97 c

10. Ex. Light acts even more strangely. Suppose a ship has a special light (made of photons) weapon: rocket's speed wrt Earth = 0.9 c speed of photon wrt to ship = c Earth The speed of the photon as measured by someone on Earth will _____________________ which would be faster than the speed of light c! Instead, it is given by: 0.9c + c = ___________ = 1 + (0.9c)(c) c 2 NOT = 1.9 c 1.9 c 1.9 c

11. ____________ 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 equivalent speed increases slow shrunken c v  c Einstein

12. "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."