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Consider a wire of uniform density and mass M shaped into a quarter circle of radius...

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Physics

Consider a wire of uniform density and mass M shaped into aquarter circle of radius R.The wire is located in the xy plane,with the origin at the focus of the quarter circle (i.e at thecenter of the circle of which the wire is part). Choose the x axisparallel to the line that connects the endpoints of the wire, sothat the y-z plane is a plane of reflection symmetry for the wire.This means that the ends of the wire are located atR/sqrt(2)*(1,1,0) and R/sqrt(2)*(-1,1,0) and that the wire can bedescribed by the equation x^2 + y^2 = R^2.

(a) Calculate the moment of inertia tensor for rotation aboutthe origin. Also calculate the location of the center of mass forthe wire.

(b) Using the results from (a) and the generalized parallelaxis theorem, find the moment of inertia tensor for rotation aboutone of the wire ends, with the x-axis along the line connecting thetwo ends of the wire. Hint: You will need to apply the theoremtwice.




please explain and answer thanks!

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