Question

Two discs of moment of inertia $I_1$ ,$I_2$ are rotating with angular velocities ${\omega }_1$, ${\omega }_2$ along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate combined along the same axis the rotational KE of system will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Let 'I' and '$\omega$' be the moment of inertia and angular velocity of the combined system of discs.

Applying conservation of angular momentum,

$I_1$ ${\omega }_1$ + $I_2$ ${\omega }_2$ = I$\omega$

$\Rightarrow$ $\omega$ = $\frac{(I_1{\omega }_1+I_2{\omega }_2)}{2(I_1+I_2)}$

$\therefore$ Rotational K.E of the system = $\frac{1}{2}$ I ${\omega }^2$ = $\frac{1}{2}$ ($I_1$ + $I_2$) $⟮\frac{(I_1{\omega }_1+I_2{\omega }_2)}{2(I_1+I_2)}{⟯}^2$
K.E = $\Rightarrow$ $\omega$ = $\frac{(I_1{\omega }_1+I_2{\omega }_2{)}^2}{2(I_1+I_2)}$