Conservation of Angular Momentum Video Lessons

Concept

# Problem: Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.53 kg·m2 and an angular velocity of +3.24 rad/s. Disk B is rotating with an angular velocity of -7.07 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 -3.27 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?

###### FREE Expert Solution

Angular momentum:

$\overline{){\mathbf{L}}{\mathbf{=}}{\mathbf{I}}{\mathbf{\omega }}}$

Conservation of angular momentum when objects come together:

$\overline{){{\mathbf{I}}}_{{\mathbf{A}}}{{\mathbf{\omega }}}_{{\mathbf{A}}}{\mathbf{+}}{{\mathbf{I}}}_{{\mathbf{B}}}{{\mathbf{\omega }}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{\left(}}{{\mathbf{I}}}_{{\mathbf{A}}}{\mathbf{+}}{{\mathbf{I}}}_{{\mathbf{B}}}{\mathbf{\right)}}{{\mathbf{\omega }}}_{{\mathbf{f}}}}$

We are given the moment of inertia of A. A is rotating in the positive direction.

We don't know the moment of inertia of B. Bis rotating in the negative direction.

When A and B are put together, they rotate in the negative direction. The angular momentum of the system is a constant (it is conserved).

Thus, we'll solve this problem using the conservation of angular momentum.

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###### Problem Details

Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.53 kg·m2 and an angular velocity of +3.24 rad/s. Disk B is rotating with an angular velocity of -7.07 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 -3.27 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?