Question

Two point P and Q diametrically opposite on a disc of radius $R$ have velocities $v$ and $2v$ as shown in figure. Find the angular speed of Q w.r.t P.

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

Answer 1

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

Angular velocity of Q w.r.t P
${\omega }_{QP}=\frac{(v_{QP}{)}_{\perp }}{PQ}$
where $(v_{QP}{)}_{\perp }$ is the velocity of Q w.r.t P perpendicular to PQ.
Here, $\text{PQ}=2R$
$(v_{QP}{)}_{\perp }=v_Q-v_P=2v-v=v$
(because the velocities are parallel to each other)
$\Rightarrow {\omega }_{QP}=\frac{v}{2R}$