Relativistic Velocity

Galilean Transformation  Relative velocity has been used since the time of Galileo. Sum velocity vectorsSum velocity vectors Relative velocity vRelative velocity v  In this transformation only the coordinate along the motion matters.

Too Fast  If A is observing B fire a probe and the sum of the speeds is low, Galilieo works.  If the sum exceeds the speed of light it would allow objects to move faster than light.

Lorentz Transformation  Using length contraction and time dilation the correct velocity can be determined.

Getaway  A starship moves at 0.75 c past an enemy base that fires lasers at the starship. An escape pod launches at 0.5 c from the starship in the same direction.  What is the velocity of the pod as seen by the base?  The speeds are given in units of c so v/c =3/4 and u/c =1/2.  The observed velocity  So, u’ = 10/11 c.

SOS  A damaged starship moves at 0.75 c past an enemy base. The starship transmits a radio beacon in the direction of its travel  What is the velocity of the beacon as seen by the base?  The beacon is electromagnetic radiation and travels at u = c.  The observed velocity  So, u’ = c.

Rebound  Consider two balls that collide. One from a platformOne from a platform One from a moving rocketOne from a moving rocket  What happens to momentum conservation?  It must hold in both frames since they are both inertial. Different momentum for time-dilated rocketDifferent momentum for time-dilated rocket

Relativistic Momentum   Classical momentum is not conserved, but relativistic momentum is.   With relativity momentum is no longer a linear relationship. next