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Standard XII

Physics

Moment of Inertia of a Disc

A round disc ...

Question

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 \omega about the same axis. The final angular velocity of the combination of discs is :-

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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\frac{I_{2}}{ω} I_{1} + I_{2}

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Solution

The correct option is A $\frac{I_{1} ω}{I_{1} + I_{2}}$
form conservation of angular momentum
$I_{1} ω$ = $(I_{1} + I_{2}) ω^{^{'}}$ $\Rightarrow ω^{^{'}}$ = $\frac{I_{1} ω}{I_{1} + I_{2}}$

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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 \omega about the same axis. The final angular velocity of the combination of discs is :-

The correct option is A I1ωI1+I2form conservation of angular momentumI1ω = (I1+I2)ω′ ⇒ω′ = I1ωI1+I2

The correct option is A $\frac{I_{1} ω}{I_{1} + I_{2}}$
form conservation of angular momentum
$I_{1} ω$ = $(I_{1} + I_{2}) ω^{^{'}}$ $\Rightarrow ω^{^{'}}$ = $\frac{I_{1} ω}{I_{1} + I_{2}}$