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Byju's Answer

Standard XII

Physics

Instantaneous Axis of Rotation

In the figure...

Question

In the figure shown, the instantaneous speed of end A of the rod is $v$ to the left. The angular velocity of the rod of length $L$ must be:

\frac{v}{2 L}

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\frac{v}{L}

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\frac{v \sqrt{3}}{2 L}

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none of these

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Solution

The correct option is A $\frac{v}{L}$
The velocities of the ends A and B along the length of rod should be the same.
Hence,
$v_{A} c o s 30^{o} = v_{B} c o s 30^{o} \Rightarrow v_{A} = v_{B} = v$
Hence, the angular velocity of the rod is
$ω = \frac{(v_{A B})_{⊥}}{L} = \frac{2 v s i n 30^{o}}{l} \Rightarrow ω = \frac{v}{L}$

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In the figure shown, the instantaneous speed of end A of the rod is v to the left. The angular velocity of the rod of length L must be:

The correct option is A vLThe velocities of the ends A and B along the length of rod should be the same.Hence,vAcos30o=vBcos30o⇒vA=vB=vHence, the angular velocity of the rod isω=(vAB)⊥L=2vsin30ol⇒ω=vL

In the figure shown, the instantaneous speed of end A of the rod is $v$ to the left. The angular velocity of the rod of length $L$ must be: