Answered: Center of mass by integrals. Find the…

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Center of mass by integrals.

Find the center of mass of a uniform wire that subtends a circular arc of radius a. as shown in the image, knowing that it has uniform density.

Please explain step by step with the complete integrals, in this exercise I do not understand why in X and in Y my teacher gives x=rcosθ y=rsenθ, when the angle in the exercise is θ/2,

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Please answer and explain.1. A uniform disk with moment of inertia at the center of mass, I1, is rotating with an initial angular speed ω1 about a frictionless shaft through its center. Another disk of moment of inertia at the center of mass, I2, is dropped from rest on top of the first disk through the same shaft. Give the angular speed of the composite two-disk system assuming that the collision is perfectly inelastic.2. Is the total energy of the rotating disk conserved in the experiment? Justify your answer using the data in Table W4. 3. In the collision of disks, the system is not isolated because of the existence of friction. How is it possible that conservation of angular momentum is still valid to a relatively good accuracy?