A uniform, solid cylinder with mass 2M and radius 2R rests on a horizontal tabletop. A massless string is attached to a massless yoke which is in turn attached to a frictionless axle that runs through the central axis of the cylinder, so that the cylinder can rotate about the axle. The string passes over a solid cylindrical pulley with mass M and radius R that is mounted on a frictionless axle. A block of mass M is suspended from the free end of the string. The string does not slip over the pulley surface, and the cylinder rolls without slipping on the tabletop. Use energy methods to derivean expression for the speed of the block after it has descended a distance d.

Up of elements with the same number of valence electrons. vertical column in the periodic table of elements such as alkali metals or halogens. a horizontal row of elements in the periodic table. this is a characteristic of the elements in the periodic table that shows a pattern. it may increase or decrease across or down the table. periodic trend these are the highly reactive elements located in group 1 of the periodic table. these elements have one electron in their outer energy level which makes them highly reactive with water and halogens. these are the reactive elements located in group 2 of the periodic table. these elements have two electrons in their outer energy level which makes them reactive with water and halogens. alkaline earth metals these are the group 3 or d-block elements. these dense metals with high boiling points can have different oxidation states and all are solid at room temperature with the exception of mercury. transition metals this is the highly reactive family of elements with 7 valence electrons. this is an element with full valence shell, very unreactive. this is a group of elements with few valence electrons that conducts heat and electricity. one of a class of elements having properties intermediate to metals and nonmetals. this is a type of element that has many valence electrons, not a conductor.