Consider the rods plus disc system shown in the Figure. The rod has a length L =0.50 m, and mass M = 0.270kg. The large disc has a radius of R = 0.130m and mass m=0.810kg. The second disk should be treated as a point mass of 0.405kg. It is glued to the rod at position X = 0.22m. The system behaves as a compound pendulum that oscillates about pivot point P. The pivot is at P where the tip of rod rod meets with one end of the disk. Assume that the disc and rod have uniform mass distributions.

Question

Consider the rods plus disc system shown in the Figure. The rod has a length L =0.50 m, and mass M = 0.270kg. The large disc has a radius of R = 0.130m and mass m=0.810kg. The second disk should be treated as a point mass of 0.405kg. It is glued to the rod at position X = 0.22m. The system behaves as a compound pendulum that oscillates about pivot point P. The pivot is at P where the tip of rod rod meets with one end of the disk. Assume that the disc and rod have uniform mass distributions.
a) Find how far below P is the center of mass of the rods and disks system. Answer in units of m.

b) Find the moment of inertia of one of the rod, in units of kgm2, as it freely rotates about the pivot point P.

c) Find the moment of inertia of the disk (the large disk), in units of kgm2, about its center of mass.

d) Find the moment of inertia of the disk (the large disk), in units of kgm2, as it freely rotates about the pivot point P.

e) Find the moment of inertia of the whole system, in units of kgm2, as it freely rotates about the pivot point P.

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