1. Finding the Center

2. Discrete Center of Mass  Discrete masses are treated as separate objects.  They can lie on a line or in a plane. m2m2 m3m3 m4m4 m1m1 r CM

3. Discrete Problem  Two trucks are on a barge. Find the center of mass. m 1 = 11 Mg, d 1 = -12 mm 1 = 11 Mg, d 1 = -12 m m 2 = 23 Mg, d 2 = +12 mm 2 = 23 Mg, d 2 = +12 m m b = 35 Mgm b = 35 Mg m2m2 mbmb d1d1 m1m1 d2d2 0 m 1 d 1 = -132 Mg mm 1 d 1 = -132 Mg m m 2 d 2 = +276 Mg mm 2 d 2 = +276 Mg m m b d b = 0m b d b = 0 M = 69 MgM = 69 Mg d CM = 2.1 md CM = 2.1 m

4. Center of Gravity  All forces act as if at the center of mass. This includes gravityThis includes gravity Sometimes called the center of gravity Sometimes called the center of gravity m2m2 m1m1

5. Symmetry  Continuous objects have a center of mass.  If an object is regular, the symmetry tells us the center along that direction.

6. Continuous Masses  In non-symmetrical directions, an integral is needed. Example, the horizontal direction in the triangleExample, the horizontal direction in the triangle next w l