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Find the moment of inertia I of a thin rod of length L and mass M a) spinning around the center axis; b) spinning around the end. T Hint: Put the rod on the x -axis and use 1 = S [P(x)]?dx where p(x) is the radial distance rod from the rotation axis of the point x along the rod. u. = M/L is the mass per length of the rod.
9.55 - CALC A slender rod with length L has a mass per unit length that varies with distance from the left end, where x = 0, according to dm/dx = yx, where y has units of kg/m². (a) Calculate the total mass of the rod in terms of y and L. (b) Use Eq. (9.20) to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Use the expression you derived in part (a) to express I in terms of Mand L. How does your result compare to that for a uniform rod? Explain. (c) Repeat part (b) for an axis at the right end of the rod. How do the results for parts (b) and (c) compare? Explain.
Find the moment of inertia about each of the following axes for a rod that is 0.200 cm in diameter and 1.20 m long, with a mass of 4.00×10^-2 kg . A) About an axis perpendicular to the rod and passing through its center. B) About an axis perpendicular to the rod and passing through one end. C) About an axis along the length of the rod.