Relativistic Velocity

1
Relativistic Velocity
2
Galilean Transformation

• Relative velocity has been used since the time of
  Galileo.
• Sum velocity vectors
• Relative velocity v

• In this transformation only the coordinate along
  the motion matters.

3
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.

4
Lorentz Transformation

• Using length contraction and time dilation the
  correct velocity can be determined.

5
Getaway

• A starship moves at 0.75c past an enemy base that
  fires lasers at the starship. An escape pod
  launches at 0.5c 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/c3/4 and
  u/c1/2.
• The observed velocity
• So, u 10/11c.

6
SOS

• A damaged starship moves at 0.75c 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.

7
Rebound

• Consider two balls that collide.
• One from a platform
• One 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 rocket

8
Relativistic Momentum

• Classical momentum is not conserved, but
  relativistic momentum is.
• With relativity momentum is no longer a linear
  relationship.

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