velocity analysis by relative velocity method

VELOCITY ANALYSIS BY RELATIVE VELOCITY METHOD

RELATIVE VELOCITY OF TWO BODIES

1. Relative Velocity of Two Bodies Moving along Parallel Lines

Consider two bodies A and B moving along parallel lines in the same direction with absolute velocities v_A and v_B, as shown in Fig.2.1(a).

Then the relative velocity of A with respect to B (Fig.2.1(b)) is given by

Similarly, the relative velocity of B with respect to A is given by

2. Relative Velocity of Two Bodies Moving along Inclined Lines

Now consider the two bodies A and B moving with absolute velocities V and v ̧, as shown in Fig.2.2(a). Then the relative velocity of A (or B) with respect to B (or A) may be obtained by (a) the triangle law of velocities or (b) the law of parallelogram of velocities.

(a) v_AB by velocity triangle (Fig.2.2(b)): Take any fixed point o representing zero velocity point. From point o, draw vector oa parallel to v and draw vector ob parallel to v to some suitable scale. Then join ab to get the velocity triangle abc. The vector ab represents the relative velocity of B with respect to A (v_BA).

The relative velocity of A with respect to B (Fig.2.2(b)) is given by

Similarly, the velocity of B with respect A is given by

(b) v_BA by velocity parallelogram (Fig.2.2(c)); Let – v_A velocity is given to both particles A and B as shown in Fig.2.2(c). When - VA is added to both particles, then particle A comes to rest; but there is no change in their relative velocity. Now the relative velocity of B with respect to A (v_BA) can be determined by drawing the parallelogram as shown in Fig.2.2(c).

vBA = v_B - v_A

Note

1. When we simply say, velocity of particle A, it refers to the absolute velocity of A (v_A)

i.e., the velocity with respect to a fixed point O (v_AO). So v_A = v_AO.

2. The relative velocity of point A with respect to B (v_AB) and the relative velocity of point B with respect to A (v_BA) are equal in magnitude but opposite in direction.