Announcements Homework Set 6: Schaum’s Outline Chapter 7 # 7.17, 7.18, 7.19, 7.24 & Plus: derive the three velocity transformation equations for u x ’ u y ’ and u z ’ starting with the basic Lorentz transformations for x’, y’, z’ and t’ and the definition of velocity: v’ x =  x’/  t’ v’ y =  y’/  t’ and v’ z =  z’/  t’ Project abstracts are due today! I will accept them via as long as they are sent by midnight. You can also post it to the Dropbox in the class D2L shell. Remember, it counts 1.5% of your course grade!

Velocity Transformations Given the velocity u of a particle with respect to observer O in the unprimed system. With the reverse transforms from primed to unprimed These can be derived from the basic transformation equations and a the definition of velocity:

Which is O, which is O’ and which is the particle? A man at the front end of a rocket ship moving past the Earth at a speed of 0.9c fires a bullet from a supergun towards the back of the rocket. He measures the speed of the bullet to be 0.5c. What does an observer on the ground measure the speed of the bullet to be? a)The rocket is O, the Earth is O’ and the bullet is the particle. b)The Earth is O, the rocket is O’ and the bullet is the particle c)The bullet is O, the rocket is O’ and the Earth is the particle d)Any of the above will work, although some are less convenient than others.

Not quite so obvious Rocket A is moving to the west at 0.9c and rocket B is moving to the east at 0.7c with respect to the Earth. What is the speed of rocket A with respect to rocket B? a)Rocket A is O, rocket B is O’ and the Earth is the particle. b)Rocket B is O, rocket A is O’ and the Earth is the particle. c)The Earth is O, rocket A is O’ and rocket B is the particle. d)The Earth is O, rocket B is O’ and rocket A is the particle. e)Any of the above will work but two are much easier than the others.

Note that transverse velocities are affected In the Galilean transformation, only u’ x is affected. The transverse velocities are the same: u’ y = u y and u’ z = u z. That is not the case for Lorentz transformations. This means that the angle at which something is moving is different for different reference frames.

Relativistic Doppler Effect For the general case where the source is moving at some angle  with respect to the observer If the motion of the source is directly towards or away from the observer then If the source is moving transverse to the observer

Watch Mechanical Universe and Beyond: Velocity and Time