The instantaneous velocity of point B of a ro | vedclass

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(D) Let the angular velocity of the rod be $\omega$. The velocity of any point $P$ on the rod at a distance $r$ from the instantaneous center of rotat

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None of these

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(D) Let the angular velocity of the rod be $\omega$. The velocity of any point $P$ on the rod at a distance $r$ from the instantaneous center of rotation $I$ is given by $v = \omega r$.For the velocity of end $A$ to be minimum, the rod must be rotating about end $A$ as the instantaneous center of rotation.The velocity of point $B$ is given as $v_B = 3 \ m/s$ at an angle of $30^{\circ}$ with the rod.The component of velocity of $B$ perpendicular to the rod is $v_{B\perp} = v_B \sin 30^{\circ}$.Since the rod is rotating about $A$, the velocity of $B$ perpendicular to the rod is also given by $v_{B\perp} = \omega L$, where $L = 0.5 \ m$ is the length of the rod.Equating the two expressions for $v_{B\perp}$:$\omega L = v_B \sin 30^{\circ}$$\omega (0.5) = 3 	imes \sin 30^{\circ}$$\omega (0.5) = 3 	imes 0.5$$\omega = 3 \ rad/s$.Since $3 \ rad/s$ is not among the options, the correct answer is $D$.

The instantaneous velocity of point $B$ of a rod of length $0.5 \ m$ is $3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. Find the angular velocity of the rod such that the velocity of end $A$ is minimum.

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