the measured moment of inertia of a system is I = 8.44 kg-m2. Assume the diamete

Question

the measured moment of inertia of a system is I = 8.44 kg-m2. Assume the diameter of the pulley around which you wrap the string is d = 2.59 cm.

a) the system is initially spinning at angular speed wo = 1.56 rad/s. After you drop a disk of mass 752 g on it, the system rotates at wf = 1.38 rad/s. Find:
- the moment of inertia of the disk:
- the radius of the disk:

b) suppose the system is initially spinning at angular speed wo = 6.06 rad/s. After you drop a cube of mass 592 g on it, the system rotates at wf = 5.13 rad/s. Find:
- the moment of inertia of the cube:
- the length of one side of the cube:

Explanation / Answer

Given initial moment of inertia of the system I1 = 8.44 kg m ^2 initial angular speed of the system 1 = 1.56 rad / s final angular speed of the system is   2 =   1.38 rad / s from conservation of angular momentum             I1 1 = I2 2      momentof inertia of disc is             I2 = I1 1   / 2                  = 8.44* 1.56 / 1.38                  = 9.54086 kg m2   moment of inertia of disc is           ( 1/2) M R 2   = 9.54086                       R2   = 9.54086 *2 / 0.752 kg    radius of disc is R = 5.0373 m   _________________________________________ b) moment of inertia of cube is               I2 = 8.44 * 6.06 / 5.13                    = 9.97 kg m^2     moment of inertia of cube is             ( 1/ 6 ) M L 2 = 9.97      length of one side is                 L = ( 9.97 * 6 / 0.592 ) ^ (1/2)                     = 10.0522 m

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