Question

A circular disk of radius r is confined to roll without slipping at P and Q as shown in the figure.

If the plates have velocities as shown, the magnitude of the angular velocity of the disk is

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

Answer 1

The correct option is A $\frac{3v}{2r}$


For pure rolling

$V_P=V=\left(PR\right)\omega ...\left(i\right)$

$V_Q=2V=\left(QR\right)\omega ...\left(ii\right)$

Divide by (ii) to (i),

$2=\frac{QR}{PR}\Rightarrow QR=2\left(PR\right)$

$PR+QR=2r$

$PR+2\left(PR\right)=2r$

$PR=\frac{2}{3}r$

From equation (i),

$V=\left(\frac{2}{3}r\right)\omega \Rightarrow =\frac{3V}{2v}$