Question

In a planar four bar mechanism the coupler AB has a length of 25cm. At a given instant the end A has velocity of 40cm/sec in the horizontal direction while the point 8 has a velocity of 30cm/sec in the vertical direction. The angular velocity of the coupler AB at the instant is

• A. 1 rad/sec
• B. 2 rad/sec
• C. 3 rad/sec
• D. zero

Answer 1

The correct option is B 2 rad/sec


$V_{AB}={\overrightarrow{V}}_B-{\overrightarrow{V}}_A=30\hat{j}-40\hat{i}$

$|{\overrightarrow{V}}_{AB}|=\sqrt{{40}^2+{30}^2}=50$

${\omega }_{AB}=\frac{|{\overrightarrow{V}}_{AB}|}{AB}=\frac{50}{25}=2rad/s$