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  4. A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane ahout an axis passing through its centre and perpendicular to the plane with an angular velocity ω Another disc of same mass hut half the radius is gently placed over it coaxially. The angular speed o f the composite disc will be

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Q. A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane ahout an axis passing through its centre and perpendicular to the plane with an angular velocity $\omega$ Another disc of same mass hut half the radius is gently placed over it coaxially. The angular speed o f the composite disc will be

Solution:

$I_1\omega_1=(I_1+I_2)\omega_2$
$\left[\frac{MR^2}{2}\right]\omega=\left[\frac{MR^2}{2}+\frac{M\left(\frac{R}{2}\right)^2}{2}\right]\omega^2$
$=\left[\frac{MR^2}{2}+\frac{MR^2}{8}\right]\omega_2=\left[\frac{5MR^2}{8}\right]$
$\omega_2=\frac{4}{5}\omega$