Question

A disc of radius $r$ has linear velocity $V$ and angular velocity $\omega$ as shown in figure. If point $B$ is at a distance $\frac{r}{2}$ from centre, then find the velocity of point $A$ w.r.t point $B$.

• A. $\omega r$
• B. $\frac{\omega r}{3}$
• C. ${\omega }^{2}r$
• D. $\frac{\omega r}{2}$

Answer 1

The correct option is D $\frac{\omega r}{2}$

As the disc rolls on the surface the
$V_A=V_{COM}+\left(\omega r_{AO}\right)\dots \dots \left(i\right)$
Similarly,
$V_B=V_{COM}+\left(\omega r_{BO}\right)\dots \dots \left(ii\right)$
$V_{AB}=V_A-V_B$
So, using equation $\left(i\right)$ and $\left(ii\right)$, we get
$V_{AB}=\omega (r_{AO}-r_{BO})$
$\Rightarrow V_{AB}=\omega r_{AB}=\frac{\omega r}{2}$