Consider two sizes of disk, both of mass M. One size of disk has radius R; the other has radius 2R. 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 equals the moment of inertia for system B, how many of the smaller disks are in system B? 1

number of smaller disks in system B = 4

Explanation:

Moment of Inertia of smaller disk is:

I_small = (1/2)MR²

Moment of inertia of larger disk is;

I_large = (1/2)M(2R)² = 2MR²

Now total moment of Inertia of system A will be 2 of the larger disk I_large

Thus, I_A = 2 x (2MR²) = 4MR²

While moment of inertia of system B will consist of 1 number of larger disk and n number of smaller disk.

Thus;

I_B = 2MR² + n((1/2)MR²)

Thus, I_B = MR²(2 + (n/2))

Since the two systems have equal moment of inertia, we will ewuate I_A to I_B. Thus,

I_A = I_B gives;

4MR² = MR²(2 + (n/2))

MR² will cancel out to give ;

4 = 2 + (n/2)

n/2 = 4 - 2

n/2 = 2

n = 4

the skeletons of most mammals reach a certain size and then stop growing. however, many animals, including some mammals, keep growing throughout their lives. kangaroos, for example, just keep growing and growing until they die. also, the longer an animal lives the greater the chance it might catch some deadly disease.