You are handed a rod that is four times as dense on one side as it is on the other side, and two times as dense in the middle as it is on the least dense side. Further, you are told that the density varies quadratically. The mass of the rod is M and the length is L. Write your answers only in terms of these constants. (a) What is the moment of inertia about an axis that passes through the midpoint of the rod (and is perpendicular to the length of the rod)?
(b) What is the moment of inertia about an axis that passes through one of the ends of the rod (and is perpendicular to the length of the rod)?

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. provide a plausible explanation for this situation (with supporting calculations) by considering a room whose air temperature is maintained at 20â°c throughout the year, while the walls of the room are nominally at 27â°c and 14â°c in the summer and winter, respectively. the exposed surface of a person in the room may be assumed to be at a temperature of 32â°c throughout the year and to have an emissivity of 0.90. the coefficient associated with heat transfer by natural convection between the person and the room air is approximately 2 w/m2 â‹…â‹… k. what is the ratio of the thermal resistance due to convection to the thermal resistance due to radiation in the summer? what is the ratio of thermal resistances in the winter

Aball tossed vertically upward from the ground next to a building passes the bottom of a window 1.8 s after being tossed and passes the top of the window 0.20 s later. the window is 2.0 m high from top to bottom. what was the ball's initial velocity? the unit vector j^ is directed upward. how far is the bottom of the window from the launch position? how high does the ball rise above the launch position?

If the wheels lock when braking suddenly the vehicle: a: loses traction b: lose steering wheel ability c: gain speed slightly d: gain steering ability