1. RELATIVE-MOTION ANALYSIS (TRANSLATING AXES)
In our previous topics, we have described particle motion using coordinates that were referred to fixed
reference axes. The displacement, velocity and accelerations so determined are termed absolute. But it
is not always possible or convenient to use a fixed set of axes for the observation of motion, and there
are many engineering problems which the analysis of motion is simplified by using measurement made
with respect to a moving reference systems.
These measurements, when combined with the absolute motion of the moving coordinate system,
permit us to determine the absolute motion in question. This approach is known as a relative-motion
analysis.
Consider particles A and B, which moves along arbitrary paths aa and bb, respectively. The absolute
position of each particle rA and rB is measured form common origin O for the fixed reference frame. The
relative position of “B with respect to A” is designated by the relative position vector rB/A. Using vector
addition:
Position: rB = rA + rB/A
Velocity: vB = vA + vB/A
Acceleration: aB = aA + aB/A
Example:
Car A is accelerating in the direction of its motion at the rate of 1.2 m/s 2. Car B is rounding a curve of
150-m radius at a constant speed of 54 km/h. Determine the velocity and acceleration that car B
appears to have to an observer in car A if car A has reached a speed of 72 km/h for the position
represented.

3. Problem:
1. A train travelling at a constant speed of 60 mi/h, crosses over a road as shown in the figure. If
automobile A is travelling at 45 mi/h along the road, determine the magnitude and direction of
the relative velocity of the train with respect to the automobile. [Ans. 42.5 mi/h, 48.5o]

4. 2. Plane A is flying along straight-line path whereas plane B is flying along a circular path having a
curvature of rB = 400 km. Determine the velocity and acceleration of B as measured by the pilot
of A. [100 km/h, 912 km/h2]
3. For the instant represented, car A has an acceleration n the direction of its motion and car B has
a speed of 72 km/h which is increasing. If the acceleration of B as observed from A is zero for
this instant, determine the acceleration of A and the rate at which the speed of B is changing.