# Relativistic Addition of Velocities

Relativistic Addition of Velocities

This Demonstration considers the composition of velocities in accordance with the special theory of relativity. Consider a system moving with velocity represented by the red arrow, with magnitude and direction , with respect to a stationary frame of reference. The red disk recapitulates this magnitude, which has an upper limit extending to the red circle, corresponding to the speed of light . The blue arrow represents a second velocity, which has a magnitude and direction , with respect to the moving frame of reference. The velocity with respect to the original stationary frame is then represented by . A compact formulation gives the components of parallel and perpendicular to : =and=The gray arrow represents the vector .

u

α

c

v

β

w=u⊕v

w

u

w

u+

v

1+u·v/

2

c

w

⊥

v

⊥

1+u·v/

2

c

1-

.2

u

2

c

w