Question

Two points $P$ and $Q$ are diametrically opposite on a disc of radius $R$. A particle at point $P$ has linear velocity $v$ as shown in figure. Find the angular speed of particle wrt an axis passing through $Q$ and perpendicular to plane of the disc.

• A. $\frac{v}{2R}$
• B. $\frac{v}{R}$
• C. $\frac{2v}{R}$
• D. $\frac{3v}{2R}$

Answer 1

The correct option is A $\frac{v}{2R}$

We have learnt that the angular velocity is given as ,
${\omega }_{PQ}=\frac{(v_{PQ}{)}_{\perp }}{r_{PQ}}$
Here $PQ=2R$ as its a diameter,
$v_{PQ}$ is the velocity of particle with respect to $Q$,

$v_{PQ}=v_P=v$
$\Rightarrow {\omega }_{PQ}=\frac{v}{2R}$

Hence option A is the correct answer.