A disc of moment of inertia I_1 is rotating with angular velocity w_1 about an axis perpendicular to its plane and passing through its centre. If another disc of moment of inertia I_2 about the same axis is gently placed over it, then the new angular velocity of the combined disc will be

  • Option 1)

    \frac{(I_1+I_2)w_1}{I_1}

  • Option 2)

    \frac{I_1w_1}{I_1+I_2}

  • Option 3)

    w_1

  • Option 4)

    \frac{I_2w_1}{I_1+I_2}

 

Answers (1)

As we discussed in

Law of conservation of angular moment -

\vec{\tau }= \frac{\vec{dL}}

- wherein

If net torque is zero

i.e. \frac{\vec{dL}}= 0

\vec{L}= constant

angular momentum is conserved only when external torque is zero .

 

 Li = L

I_Iw_I =(I_I+I_2)w_2

 

w_2=\frac{I_1w_1}{I_1+I_2}


Option 1)

\frac{(I_1+I_2)w_1}{I_1}

incorrect

Option 2)

\frac{I_1w_1}{I_1+I_2}

correct

Option 3)

w_1

incorrect

Option 4)

\frac{I_2w_1}{I_1+I_2}

incorrect

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