Consider a wire of uniform density and mass M shaped into a quarter 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 the center of the circle of which the wire is part). Choose the x axis parallel to the line that connects the endpoints of the wire, so that the y-z plane is a plane of reflection symmetry for the wire. This means that the ends of the wire are located at R/sqrt(2)*(1,1,0) and R/sqrt(2)*(-1,1,0) and that the wire can be described by the equation x^2 + y^2 = R^2. Required:
a. Calculate the moment of inertia tensor for rotation about the origin. Also calculate the location of the center of mass for the wire.
b. Using the results from (a) and the generalized parallel axis theorem, find the moment of inertia tensor for rotation about one of the wire ends, with the x-axis along the line connecting the two ends of the wire.

Amajor impediment to wide acceptance of electric vehicles even on the part of people who use their cars almost exclusively for commuting is the inability to use their electric vehicles for occasional extended trips. in an attempt to make purchasing electric vehicles more attractive to commuters, one electric vehicle producer is planning to offer customers three days free rental of a conventional car for every 1,000 miles that they drive their electric vehicle. which of the following, if true, most threatens the plan's prospects for success? (a) many electric vehicles that are used for commercial purposes are not needed for extended trips. (b) because a majority of commuters drive at least 100 miles a week, the cost to the producer of making good the offer would add considerably to the already high price of electric vehicles. (c) the relatively long time it takes to recharge the battery of an electric vehicle can easily be fitted into the regular patterns of car use characteristic of commuters. (d) although electric vehicles are essentially emission-free in actual use, generating the electricity necessary for charging an electric vehicle's battery can burden the environment. (e) some family vehicles are used primarily not for commuting but for making short local trips, such as to do errands.