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 d

Question

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

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Hải Đăng 2 months 2021-07-22T14:59:01+00:00 1 Answers 3 views 0

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    2021-07-22T15:00:29+00:00

    Answer:

    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

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