Classical addition of velocities¶

The law of classical addition of velocities, usually attributed to Galileo and called the Galilean law of velocity addition, states that the velocity of a body in an inertial reference frame \(A\) can be found as a sum of its velocity in another inertial reference frame \(B\) and the velocity of frame \(B\) relative to frame \(A\).

Conditions:

Velocity vectors must be collinear.
Space and time are absolute.
Applicable to inertial reference frames.

Links:

Wikipedia, vector counterpart of this law.

body_speed_in_first_frame¶: speed of the body in frame \(A\).

Symbol:: v_OA
Latex:: \(v_{OA}\)
Dimension:: velocity

body_speed_in_second_frame¶: speed of the body in frame \(B\).

Symbol:: v_OB
Latex:: \(v_{OB}\)
Dimension:: velocity

second_frame_speed_in_first_frame¶: speed of frame \(B\) relative to frame \(A\).

Symbol:: v_BA
Latex:: \(v_{BA}\)
Dimension:: velocity

law¶

v_OA = v_OB + v_BA

Latex:: \[v_{OA} = v_{OB} + v_{BA}\]