A round disc of moment of inertia $I_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_{1}$ rotating with an angular velocity $ω$ about the same axis. The final angular velocity of the combination of disc is

\frac{I_{2} ω}{I_{1} + I_{2}}

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ω

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\frac{I_{1} ω}{I_{1} + I_{2}}

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\frac{(I_{1} + I_{2}) ω}{I_{1}}

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Solution

The correct option is B $\frac{I_{1} ω}{I_{1} + I_{2}}$
Total angular momentum of the system initially $L_{i} = I_{1} w + I_{2} (0) = I_{1} w$
Total angular momentum of the system finally $L_{f} = (I_{1} + I_{2}) w_{2}$
According to conservation of angular momentum i.e. $L_{i} = L_{f}$
$\Rightarrow I_{1} ω = (I_{1} + I_{2}) ω_{2}$
$\Rightarrow ω_{2} = \frac{I_{1} ω}{I_{1} + I_{2}}$

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A round disc of moment of inertia I2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I1 rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of disc is

The correct option is B I1ωI1+I2Total angular momentum of the system initially Li=I1w+I2(0)=I1wTotal angular momentum of the system finally Lf=(I1+I2)w2According to conservation of angular momentum i.e. Li=Lf⇒I1ω=(I1+I2)ω2⇒ω2=I1ωI1+I2

A round disc of moment of inertia $I_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_{1}$ rotating with an angular velocity $ω$ about the same axis. The final angular velocity of the combination of disc is