Athin uniform rectangular plate (lamina) is of mass m and dimensions 2a by a. choose a coordinate system oxyz such that the plate lies in the xy plane with origin at a corner, the long dimension being along the x-axis. find the following: (a) the moment of inertia tensor about the origin (b) the principal moments of inertia about the origin (c) the angular momentum about the origin if the plate is spinning with angular rate about the diagonal through the origin cottcides wnth he 0in rehret to an ineria frame of wich the onigin coincides with the oxyz system.

How much work would a child do while puling a 12-kg wagon a distance of 3m with a 22 n force directed 30 degrees with respect to the horizontal? (a) 82j (b) 52j (c) 109j (d) 95j

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

Looking at this barometer, is the air pressure high or low? what type of weather would you expect? high, bad low, bad high, good low, good