Two discs of moment of inertia ' I 1 ' and ' I 2 ' and angular speeds ' ω 1 ' and ' ω 2 ' are rotating in the same direction along the collinear axes pa

Question

Two discs of moment of inertia ' I 1 ​ ' and ' I 2 ​ ' and angular speeds ' ω 1 ​ ' and ' ω 2 ​ ' are rotating in the same direction along the collinear axes passing through their centre of mass and perpendicular to their plane. If the two discs are made to rotate together along the same axis. The rotational kinetic energy of the system will be

TestHub · Accepted Answer

By the principle of conservation of angular momentum, the total initial angular momentum is equal to the total final angular momentum.

$L_{i} = L_{f}$

$I_{1} ω_{1} + I_{2} ω_{2} = (I_{1} + I_{2}) ω$

$ω = \frac{I _{1} ω _{1} + I _{2} ω _{2}}{I _{1} + I _{2}}$

The final rotational kinetic energy of the system is given by:

$K_{f} = \frac{1}{2} (I_{1} + I_{2}) ω^{2}$

Substituting the value of $ω$ :

$K_{f} = \frac{1}{2} (I_{1} + I_{2}) (\frac{I _{1} ω _{1} + I _{2} ω _{2}}{I _{1} + I _{2}})^{2}$

$K_{f} = \frac{( I _{1} ω _{1} + I _{2} ω _{2} ) ^{2}}{2 ( I _{1} + I _{2} )}$

Answer: $\frac{( I _{1} ω _{1} + I _{2} ω _{2} ) ^{2}}{2 ( I _{1} + I _{2} )}$

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion