Question

When disc $B$ is brought in contact with disc $A$, they acquire a common angular velocity in time $t$. The average frictional torque on one disc by the other during this period is

• A. $\frac{2I\omega }{3t}$
• B. $\frac{9I\omega }{2t}$
• C. $\frac{9I\omega }{4t}$
• D. $\frac{3I\omega }{2t}$

Answer 1

The correct option is A $\frac{2I\omega }{3t}$

Applying conservation of angular momentum

$I\left(2\omega \right)\to 2I\left(\omega \right)=3I{\omega }^1$

${\omega }^1=\frac{4I\omega }{3I}$

${\omega }^1=\frac{4}{3}\omega$

Them, using the equation of circular motion

${\omega }^1\omega +\frac{I}{2I}t$ [$t=2I\omega$]

$\frac{4\omega }{3}=\omega +\frac{T}{2I}T$

$\frac{1}{3}\omega =\frac{T}{2I}t$

$t=\frac{2ICO}{3t}$