Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.

Question

Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.3 kg · m2 and an angular velocity of +6.5 rad/s. Disk B is rotating with an angular velocity of -10 rad/s. The two disks are then linked together without the aid of any external torques, so that they rotate as a single unit with an angular velocity of -2.1 rad/s. The axis of rotation for this unit is the same as that for the separate disks. What is the moment of inertia of disk B?
kg · m2

Explanation / Answer

Given that Ia = 3.3 kg-m2 a = 6.5 rad/s b = -10 rad/s After linked = -2.1 rad/s Therefore According to conservation of angular momentum, we have            Ia a + Ib b = Ia + Ib ==>   Ia (a - ) = Ib ( - b) ==>   Ib = Ia (a - ) / ( - b)                = 3.3 (6.5 - (-2.1) ) / ( (-2.1) - (-10) )                = 3.592 kg-m2

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