Relative Motion (Relative Velocity) in One and Two Dimensions
First: Summary:
❶ Reference Frame
A reference frame is a coordinate system (𝑥 − 𝑦) whose origin represents the reference point (the observer
of the motion is the reference point).
Reference frames can be stationary relative to each other, like observers in two different houses, or moving
relative to each other, like one observer standing on the ground and another riding in a moving car.
Frames that move at a constant velocity relative to each other are called inertial frames, which are the
frames we will work with.
Galileo’s Principle of Relativity:
The laws of mechanics are valid in all inertial frames, although the value of velocity may differ from one
frame to another.
❷ Relative Velocity
The relative velocity of a body in one reference frame with respect to another frame is given by:
𝑣⃗𝐴/𝐶 = 𝑣⃗𝐴/𝐵 + 𝑣⃗𝐵/𝐶
where:
𝑣⃗𝐴/𝐶 : The velocity of body (𝐴) relative to reference frame (𝐶).
𝑣⃗𝐴/𝐵 : The velocity of body (𝐴) relative to reference frame (𝐵).
𝑣⃗𝐵/𝐶 : The velocity of reference frame (𝐵) relative to reference frame (𝐶).
Notes:
► The addition in this formula is vector addition, meaning that the directions must be carefully considered
when substituting values.
► In most problems, (𝐵) represents the moving reference frame, and (𝐶) represents the ground or the
stationary frame.
A
body
Moving
frame B
C
stationary
frame
First: Summary:
❶ Reference Frame
A reference frame is a coordinate system (𝑥 − 𝑦) whose origin represents the reference point (the observer
of the motion is the reference point).
Reference frames can be stationary relative to each other, like observers in two different houses, or moving
relative to each other, like one observer standing on the ground and another riding in a moving car.
Frames that move at a constant velocity relative to each other are called inertial frames, which are the
frames we will work with.
Galileo’s Principle of Relativity:
The laws of mechanics are valid in all inertial frames, although the value of velocity may differ from one
frame to another.
❷ Relative Velocity
The relative velocity of a body in one reference frame with respect to another frame is given by:
𝑣⃗𝐴/𝐶 = 𝑣⃗𝐴/𝐵 + 𝑣⃗𝐵/𝐶
where:
𝑣⃗𝐴/𝐶 : The velocity of body (𝐴) relative to reference frame (𝐶).
𝑣⃗𝐴/𝐵 : The velocity of body (𝐴) relative to reference frame (𝐵).
𝑣⃗𝐵/𝐶 : The velocity of reference frame (𝐵) relative to reference frame (𝐶).
Notes:
► The addition in this formula is vector addition, meaning that the directions must be carefully considered
when substituting values.
► In most problems, (𝐵) represents the moving reference frame, and (𝐶) represents the ground or the
stationary frame.
A
body
Moving
frame B
C
stationary
frame
