A disc of moment of inertia \(I_1\) is rotating with an angular velocity \(\omega_1\). Another disc of…
A disc of moment of inertia \(I_1\) is rotating with an angular velocity \(\omega_1\). Another disc of moment of inertia \(I_2\) which is not rotating, is gently put on the first disc. The angular speed of the system will be
\(\left(\frac{l_1+I_2}{l_1}\right) \omega_1\)
\(\left(\frac{I_1}{I_1+I_2}\right) \omega_1\)
\(\left(\frac{l_1-I_2}{l_1}\right) \omega_1\)
\(\left(\frac{I_1}{I_1-I_2}\right) \omega_1\)
Solution
Since, no external torque acts on the system, hence by the law of conservation of angular momentum,
\(\begin{aligned}
& I_1 \omega_1=\left(I_1+I_2\right) \omega_2 \\
& {\left[\omega_2=\text { final angular velocity of system }\right] } \\
\Rightarrow \quad & \omega_2=\left(\frac{I_1}{I_1+I_2}\right) \omega_1
\end{aligned}\)