Question

In: Physics

A disk of mass M is spinning freely at 9.11 rad/s when a second identical disk,...

A disk of mass M is spinning freely at 9.11 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating.

A. What is the angular speed of the new system (in rad/s)

B. If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s)

Expert Solution

(A)

Let be the moment of inertia of single disc. Initial angular momentum of the system is

The moment of inertia of the two disc is

Let be the angular momentum of the two system of two disc, the angular momentum of the system of the two discs when they are corotating is

By the conservation of angular momentum before and after the second disc was dropped.

(B)

The moment of inertia of the three discs is

The angular momentum of the system of three discs is

By the conservation of angular momentum before and after the third disc was thrown

genius_generous answered 2 years ago

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