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In addition to the revision notes for Relative Motion on this page, you can also access the following Kinematics learning resources for Relative Motion
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 3.13 | Relative Motion |
In these revision notes for Relative Motion, we cover the following key points:
The motion of an object does not depend only on the values of its kinematic quantities but also on the reference frame chosen to study its motion. Therefore, we say "the motion is relative; its parameters may be different in two different reference frames although the rhythm of motion may be the same."
When two objects are moving towards to or away from each other, one of the objects is taken as a reference frame and the other as a normal moving object. Said this, there are six possible cases regarding the objects involved in a relative motion. They are:
This includes the situations described in Uniform Motion explained in the previous tutorials. Thus, if the initial position of the object is x⃗0 units to the reference point and the object is moving at constant velocity v⃗, the equation of motion which gives the position x⃗ of the object at any instant t, is
In this case, the object's velocity is v⃗ = 0 but the reference frame's velocity is v⃗'. If the reference frame is moving let's say due right (in the positive direction), the object seems moving due left (in the negative direction), although it is at rest.
If the object is initially at x⃗0, after t seconds, it will be at
Since the object is at rest (v⃗ = 0), the second term of the above equation is cancelled, so we obtain
where v⃗' is the velocity by which the reference frame is moving.
This is the case when two objects are moving either in the same or in the opposite direction. One of the objects is taken as a reference frame (for example the car in which we are inside) and the other object is considered as an object moving in respect to the first. Once again, we use the equation (2)
to find the position of the second object in respect to the first one (the reference frame).
This case represents the situations described earlier in tutorials involving motion with constant acceleration. Thus, since v⃗' = 0, we obtain for the position of an object at any instant t (if the object which initially was at x⃗0 and it is moving at constant acceleration a⃗):
or
since v⃗' = 0 and as a result, the last term of equation (3) is cancelled.
In this case, the last term of the equation (3) is not cancelled but it is an active term of the equation. Thus, we have:
Factorizing, we obtain
Depending on the direction of motion of the object and reference frame, we have
where,
We can also use the help of relative kinematic quantities to approach the abovementioned situations. Hence, we can write v⃗rel instead of v⃗ - v⃗', v⃗0(rel) instead of v⃗0 - v⃗0' and a⃗rel instead of a⃗ - a⃗' in all exercises involving the relative motion. In this way, the calculations become easier and shorter.
Relative quantities can be used in other equations of motion with constant acceleration as well. Therefore, we can write
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