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A rigid link PQ is undergoing plane motion as shown in the figure (Vp and VQ are non-zero). VQP is the relative velocity of point Q with respect to point P. Which one of the following is TRUE?

1. VQP has components along and perpendicular to PQ
2. VQP has only one component directed from P to Q
3. VQP has only one component directed from Q to P
4. VQP has only one component perpendicular to PQ

Correct answer: VQP has only one component perpendicular to PQ

Solution

In plane motion of a rigid link, the relative velocity between two points on the link can be analyzed using the concept of instantaneous rotation about a point. Since the link is rigid, the relative velocity VQP must be perpendicular to the line connecting points P and Q, which means it has only one component that is perpendicular to PQ.

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