1. Tardigrade
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  3. Physics
  4. A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω . Another disc of same dimensions but of mass M / 4 is placed gently on the first disc coaxially. The angular velocity of the system now is

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Q. A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega .$ Another disc of same dimensions but of mass $M / 4$ is placed gently on the first disc coaxially. The angular velocity of the system now is

System of Particles and Rotational Motion

Solution:

As no torque is applied, therefore angular momentum is conserved.
$\therefore I_{1} \omega_{1}=I_{2} \omega_{2}$
$\text { or } \omega_{2}=\frac{I_{1} \omega_{1}}{I_{2}}=\frac{\left(\frac{1}{2} M R^{2}\right) \omega}{\left(\frac{1}{2} M R^{2}+\frac{1}{2} \frac{M}{4} R^{2}\right)}=\frac{4 \omega}{5}$