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 +6.6 rad/s. Disk B is rotating with an angular velocity of -9.3 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?

Answer 1

The angular momentum of a rotation object is the product of its moment of inertia and its angular velocity:

L = Iω

L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Apply the conservation of angular momentum. The total angular momentum before disks A and B are joined is:

L_{before} = (3.3)(6.6) + B(-9.3)

L_{before} = -9.3B+21.78

where B is the moment of inertia of disk B.

The total angular momentum after the disks are joined is:

L_{after} = (3.3+B)(-2.1)

L_{after} = -2.1B-6.93

L_{before} = L_{after}

-9.3B + 21.78 = -2.1B - 6.93

B = 4.0kg·m²

The moment of inertia of disk B is 4.0kg·m²