In many situations, there is a need to examine the motion of two or more points relative to each other.

Consider two points, A and B, both in motion relative to the origin O. This section will examine the motion of B relative to A.

Position

If r_{B/A} is the position vector of B relative to A, then it can be stated that

r_{B} = r_{A} + r_{B/A}

This is simply adding two position vectors to get a new total vector. This is illustrated in the diagram at the left.

Velocity

To find the relative velocities of two points, take the time derivative of the position, giving

d(r_{B})/dt = d(r_{A} + r_{B/A})/dt

v_{B} = v_{A} + v_{B/A}

Acceleration

Relative acceleration is found by taking the time derivative of the
velocity,

d(v_{B})/dt = d(v_{A}
+ v_{B/A})/dt

a_{B} = a_{A} + a_{B/A}

Practice Homework and Test problems now available in the 'Eng Dynamics' mobile app
Includes over 400 problems with complete detailed solutions.
Available now at the
Google Play Store and
Apple App Store.