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Question

A rigid link PQ of length 3 m is moving in space as shown in the figure. The magnitude and direction of velocity at point Q and direction of velocity at point P are given. Find magnitude of velocity at point P at this instant.

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Answer

Link PQ is in General Plane Motion, we can find velocity any point on link PQ  by locating instantaneous center of rotation of link PQ.

To locate instantaneous centre of rotation, follow these steps:

 (1)Choose any two points on the rod ,

(2)Draw velocity vectors of these two points.

 (3) Draw perpendiculars to the velocity vectors, wherever these two perpendiculars intersect that gives the instantaneous centre of rotation of the rod.

Since velocity vectors at points P and Q are given in the question, draw perpendiculars to the velocity vectors at points P and Q to locate instantaneous center of rotation of the rod (point O) as shown in Figure 1.

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At this instant the rod PQ is rotating about point O.

Therefore, we have

V= (OP) (ɷ)……………...Equation (1)

V= (OQ)(ɷ)……………. Equation (2)

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Velocity of point P at this instant  is  2 m/s.