Question

A uniform disk (m = 2 kg, r = 50 cm) is rotating at an angular speed 480 rpm. A second disk (m = 1 kg, r = 160 cm) is rotating at speed 360 rpm. Now first disk is dropped gently on second disk & they eventually rotate together about common axis. Find final angular velocity in rad/s.

• A. 12.6 $\pi$
• B. 11.2$\pi$
• C. 22.4 $\pi$
• D. 6.4 $\pi$

Answer 1

The correct option is A 12.6 $\pi$


$L_1=I_1{\omega }_1$
$L_2=I_2{\omega }_2$ $L_{system}=I_1{\omega }_1+I_2{\omega }_2$
At equilibrium

$L^{\prime \prime }=(I_1+I_2)\omega$
Now $L_1+L_2=L^{\prime \prime }$
$\omega =\frac{I_1{\omega }_1+I_2{\omega }_2}{I_1+I_2}$

${\omega }_1=480rpm=16\pi rad/s$
${\omega }_2=360rpm=12\pi rad/s$
$I_1=\frac{1}{2}\times 2\times {0.5}^2=0.25kg{m}^2{I}_2=\frac{1}{2}\times 1\times {1.6}^2=1.28kg{m}^2$
$Substitutethevaluestoget,\omega =12.6\pi rad/s$