a, b, and c 1. A non-uniform beam is located along the x axis from x = 0 to x = L and linearx2mass density of 1 = 20- (Note: "linear mass density" means dm = AdL,L2much like "volume mass density" means dm = pdV or "area mass densitymeans dm = odA.)a. Find the total mass of the beam.b. Find the center of mass of the beam. Compare this to the answer you wouldhave gotten for a uniform beam and explain why this result makes sense.c. Find the moment of inertia of the beam about the y axis.d. Assume that the beam is pinned at the origin. By breaking the beam into abunch of differential mass elements dm of width dx, find the total torquecreated by the beam about the origin by adding up (integrating) the torquecreated by each of the dm's.e. Show that this torque is equivalent to concentrating the entire mass of thebeam at the center of mass and then calculating the torque. This is one of thereasons we use the center of mass of an object.

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1. A non-uniform beam is located along the x axis from x = 0 to x = L and linear mass density of 1 = 20. (Note: "linear mass density" means dm = ìdL, much like "volume mass density" means dm = pdV or “area mass density means dm = odA.) a. Find the total mass of the beam. b. Find the center of mass of the beam. Compare this to the answer you would have gotten for a uniform beam and explain why this result makes sense. c. Find the moment of inertia of the beam about the y axis.

1. A non-uniform beam is located along the x axis from x = 0 to x = L and linear mass density of 1 = 20. (Note: "linear mass density" means dm = ìdL, much like "volume mass density" means dm = pdV or “area mass density means dm = odA.) a. Find the total mass of the beam. b. Find the center of mass of the beam. Compare this to the answer you would have gotten for a uniform beam and explain why this result makes sense. c. Find the moment of inertia of the beam about the y axis.