Center of Mass The rules of dynamics and momentum apply to systems as a whole just as they do to bodies.

Rotation of a Rigid Body RIGID BODY is an extended object whose size and shape do NOT change as it moves.

Center of Mass The center of mass of a system is the point at which all the mass can be assumed to reside. Sometimes the system is a group of particles and sometimes it is a solid object. Mathematically, you can think of the center of mass as a “weighted average”.

Center of Mass of an irregular shaped object can be experimentally determined using a plumb bob. CM is where all the plumb bob lines intersect

Center of Mass Average location of mass. An object can be treated as though all its mass were located at the CM. 10kg 2kg X 2m CM Note: Pick origin and center of one of the masses.

Problem: Determine the x- and y- coordinates of the Center of Mass X

Center of Mass and Collisions Since there is no net force on the system of colliding particles v CM = constant p CM = constant

Center of Mass: A fisherman stands at the back of a perfectly symmetrical boat of length L. The boat is at rest in the middle of a perfectly still and peaceful lake, and the fisherman has a mass 1 / 4 that of the boat. If the fisherman walks to the front of the boat, by how much is the boat displaced? Boat moves x fC -x iC = 3L/10 - L/2 = -L/5 X X x iC =L/2 X x fC Since there is no net force on the system of canoe and man, x CM does not move

Center of Mass and Equilibrium When CM is in same line as pivot point of object or lies directly above the footprint, object is in static equilibrium X X X STABLE UNSTABLE

Center of Mass and Equilibrium When CM is below pivot point of object, it is nearly impossible to topple