Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0 .

Question

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0 . 1 kg - m 2 and 10 rad s - 1 respectively while those for the second one are 0 . 2 kg - m 2 and 5 rad s - 1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is :

TestHub · Accepted Answer

Common angular velocity from angular momentum conversation

$ω = \frac{l_{1} ω_{1} + I_{2} ω_{2}}{I_{1} + I_{2}} = \frac{0.1 \times 10 + 0.2 \times 5}{0.1 + 0.2} = \frac{20}{3}$
Final K.E.
$K_{f} = \frac{1}{2} I_{1} ω^{2} + \frac{1}{2} I_{2} ω^{2}$
$= \frac{1}{2} (0.1 + 0.2) \times {(\frac{20}{3})}^{2} \Rightarrow k_{f} = \frac{20}{3}$

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