Consider two sizes of disk, both of mass M. One size of disk has radius R; the other has radius 4R. System A consists of two of the larger disks rigidly connected to each other with a common axis of rotation. System B consists of one of the larger disks and a number of the smaller disks rigidly connected with a common axis of rotation. If the moment of inertia for system A = the moment of inertia for system B, how many of the smaller disks are in system B? 1 4 10 16

Question

Mathematics

Caitlin

30 November, 21:33

Consider two sizes of disk, both of mass M. One size of disk has radius R; the other has radius 4R. System A consists of two of the larger disks rigidly connected to each other with a common axis of rotation. System B consists of one of the larger disks and a number of the smaller disks rigidly connected with a common axis of rotation. If the moment of inertia for system A = the moment of inertia for system B, how many of the smaller disks are in system B? 1 4 10 16

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Susan Quinn · Answer 1

16

Step-by-step explanation:

Moment of inertia of a disk is proportional to its mass and to the square of its radius. For two disks with the same mass, the larger one will have a moment of inertia that is (4R/R) ^2 = 16 times that of the smaller one.

It will take 16 smaller disks to make the systems have the same moment of inertia.